## Statistics (stat) updates on the arXiv.org e-print archive



To study radiotherapy-related adverse effects, detailed dose information (3D distribution) is needed for accurate dose-effect modeling. For childhood cancer survivors who underwent radiotherapy in the pre-CT era, only 2D radiographs were acquired, thus 3D dose distributions must be reconstructed. State-of-the-art methods achieve this by using 3D surrogate anatomies. These can however lack personalization and lead to coarse reconstructions. We present and validate a surrogate-free dose reconstruction method based on Machine Learning (ML). Abdominal planning CTs (n=142) of recently-treated childhood cancer patients were gathered, their organs at risk were segmented, and 300 artificial Wilms' tumor plans were sampled automatically. Each artificial plan was automatically emulated on the 142 CTs, resulting in 42,600 3D dose distributions from which dose-volume metrics were derived. Anatomical features were extracted from digitally reconstructed radiographs simulated from the CTs to resemble historical radiographs. Further, patient and radiotherapy plan features typically available from historical treatment records were collected. An evolutionary ML algorithm was then used to link features to dose-volume metrics. Besides 5-fold cross validation, a further evaluation was done on an independent dataset of five CTs each associated with two clinical plans. Cross-validation resulted in mean absolute errors $\leq$0.6 Gy for organs completely inside or outside the field. For organs positioned at the edge of the field, mean absolute errors $\leq$1.7 Gy for $D_{mean}$, $\leq$2.9 Gy for $D_{2cc}$, and $\leq$13% for $V_{5Gy}$ and $V_{10Gy}$, were obtained, without systematic bias. Similar results were found for the independent dataset. To conclude, our novel organ dose reconstruction method is not only accurate, but also efficient, as the setup of a surrogate is no longer needed.

Policy evaluation is a key process in Reinforcement Learning (RL). It assesses a given policy by estimating the corresponding value function. When using parameterized value functions, common approaches minimize the sum of squared Bellman temporal-difference errors and receive a point-estimate for the parameters. Kalman-based and Gaussian-processes based frameworks were suggested to evaluate the policy by treating the value as a random variable. These frameworks can learn uncertainties over the value parameters and exploit them for policy exploration. When adopting these frameworks to solve deep RL tasks, several limitations are revealed: excessive computations in each optimization step, difficulty with handling batches of samples which slows training and the effect of memory in stochastic environments which prevents off-policy learning. In this work, we discuss these limitations and propose to overcome them by an alternative general framework, based on the extended Kalman filter. We devise an optimization method, called Kalman Optimization for Value Approximation (KOVA) that can be incorporated as a policy evaluation component in policy optimization algorithms. KOVA minimizes a regularized objective function that concerns both parameter and noisy return uncertainties. We analyze the properties of KOVA and present its performance on deep RL control tasks.

Impersonators on Online Social Networks such as Instagram are playing an important role in the propagation of the content. These entities are the type of nefarious fake accounts that intend to disguise a legitimate account by making similar profiles. In addition to having impersonated profiles, we observed a considerable engagement from these entities to the published posts of verified accounts. Toward that end, we concentrate on the engagement of impersonators in terms of active and passive engagements which is studied in three major communities including Politician'', News agency'', and Sports star'' on Instagram. Inside each community, four verified accounts have been selected. Based on the implemented approach in our previous studies, we have collected 4.8K comments, and 2.6K likes across 566 posts created from 3.8K impersonators during 7 months. Our study shed light into this interesting phenomena and provides a surprising observation that can help us to understand better how impersonators engaging themselves inside Instagram in terms of writing Comments and leaving Likes.

Graph neural networks (GNNs) have achieved outstanding performance in learning graph-structured data. Many current GNNs suffer from three problems when facing large-size graphs and using a deeper structure: neighbors explosion, node dependence, and oversmoothing. In this paper, we propose a general subgraph-based training framework, namely Ripple Walk Training (RWT), for deep and large graph neural networks. RWT samples subgraphs from the full graph to constitute a mini-batch and the full GNN is updated based on the mini-batch gradient. We analyze the high-quality subgraphs required in a mini-batch in a theoretical way. A novel sampling method Ripple Walk Sampler works for sampling these high-quality subgraphs to constitute the mini-batch, which considers both the randomness and connectivity of the graph-structured data. Extensive experiments on different sizes of graphs demonstrate the effectiveness of RWT in training various GNNs (GCN & GAT).

The multi-armed bandit formalism has been extensively studied under various attack models, in which an adversary can modify the reward revealed to the player. Previous studies focused on scenarios where the attack value either is bounded at each round or has a vanishing probability of occurrence. These models do not capture powerful adversaries that can catastrophically perturb the revealed reward. This paper investigates the attack model where an adversary attacks with a certain probability at each round, and its attack value can be arbitrary and unbounded if it attacks. Furthermore, the attack value does not necessarily follow a statistical distribution. We propose a novel sample median-based and exploration-aided UCB algorithm (called med-E-UCB) and a median-based $\epsilon$-greedy algorithm (called med-$\epsilon$-greedy). Both of these algorithms are provably robust to the aforementioned attack model. More specifically we show that both algorithms achieve $\mathcal{O}(\log T)$ pseudo-regret (i.e., the optimal regret without attacks). We also provide a high probability guarantee of $\mathcal{O}(\log T)$ regret with respect to random rewards and random occurrence of attacks. These bounds are achieved under arbitrary and unbounded reward perturbation as long as the attack probability does not exceed a certain constant threshold. We provide multiple synthetic simulations of the proposed algorithms to verify these claims and showcase the inability of existing techniques to achieve sublinear regret. We also provide experimental results of the algorithm operating in a cognitive radio setting using multiple software-defined radios.

To make decisions based on a model fit by Auto-Encoding Variational Bayes (AEVB), practitioners typically use importance sampling to estimate a functional of the posterior distribution. The variational distribution found by AEVB serves as the proposal distribution for importance sampling. However, this proposal distribution may give unreliable (high variance) importance sampling estimates, thus leading to poor decisions. We explore how changing the objective function for learning the variational distribution, while continuing to learn the generative model based on the ELBO, affects the quality of downstream decisions. For a particular model, we characterize the error of importance sampling as a function of posterior variance and show that proposal distributions learned with evidence upper bounds are better. Motivated by these theoretical results, we propose a novel variant of the VAE. In addition to experimenting with MNIST, we present a full-fledged application of the proposed method to single-cell RNA sequencing. In this challenging instance of multiple hypothesis testing, the proposed method surpasses the current state of the art.

The choice of activation function can have a large effect on the performance of a neural network. While there have been some attempts to hand-engineer novel activation functions, the Rectified Linear Unit (ReLU) remains the most commonly-used in practice. This paper shows that evolutionary algorithms can discover novel activation functions that outperform ReLU. A tree-based search space of candidate activation functions is defined and explored with mutation, crossover, and exhaustive search. Experiments on training wide residual networks on the CIFAR-10 and CIFAR-100 image datasets show that this approach is effective. Replacing ReLU with evolved activation functions results in statistically significant increases in network accuracy. Optimal performance is achieved when evolution is allowed to customize activation functions to a particular task; however, these novel activation functions are shown to generalize, achieving high performance across tasks. Evolutionary optimization of activation functions is therefore a promising new dimension of metalearning in neural networks.

Many sequence-to-sequence generation tasks, including machine translation and text-to-speech, can be posed as estimating the density of the output y given the input x: p(y|x). Given this interpretation, it is natural to evaluate sequence-to-sequence models using conditional log-likelihood on a test set. However, the goal of sequence-to-sequence generation (or structured prediction) is to find the best output y^ given an input x, and each task has its own downstream metric R that scores a model output by comparing against a set of references y*: R(y^, y* | x). While we hope that a model that excels in density estimation also performs well on the downstream metric, the exact correlation has not been studied for sequence generation tasks. In this paper, by comparing several density estimators on five machine translation tasks, we find that the correlation between rankings of models based on log-likelihood and BLEU varies significantly depending on the range of the model families being compared. First, log-likelihood is highly correlated with BLEU when we consider models within the same family (e.g. autoregressive models, or latent variable models with the same parameterization of the prior). However, we observe no correlation between rankings of models across different families: (1) among non-autoregressive latent variable models, a flexible prior distribution is better at density estimation but gives worse generation quality than a simple prior, and (2) autoregressive models offer the best translation performance overall, while latent variable models with a normalizing flow prior give the highest held-out log-likelihood across all datasets. Therefore, we recommend using a simple prior for the latent variable non-autoregressive model when fast generation speed is desired.

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, in some specific cases the interest involves the effects of latent factors not only in the mean, but in the entire response distribution, represented by a quantile. This paper introduces a new class of models, named quantile factor models, which combines factor model theory with distribution-free quantile regression producing a robust statistical method. Bayesian estimation for the proposed model is performed using an efficient Markov chain Monte Carlo algorithm. The proposed model is evaluated using synthetic datasets in different settings, in order to evaluate its robustness and performance under different quantiles compared to more usual methods. The model is also applied to a financial sector dataset and a heart disease experiment.

Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded adversarial perturbations. However, how to train a good base classifier that is accurate and robust when smoothed has not been fully investigated. In this work, we derive a new regularized risk, in which the regularizer can adaptively encourage the accuracy and robustness of the smoothed counterpart when training the base classifier. It is computationally efficient and can be implemented in parallel with other empirical defense methods. We discuss how to implement it under both standard (non-adversarial) and adversarial training scheme. At the same time, we also design a new certification algorithm, which can leverage the regularization effect to provide tighter robustness lower bound that holds with high probability. Our extensive experimentation demonstrates the effectiveness of the proposed training and certification approaches on CIFAR-10 and ImageNet datasets.

Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local neighborhood of nodes and fail to capture the global graph structure, i.e. to retain the relations to distant nodes. To counter that problem, we propose a novel extension to random walk based graph embedding, which removes a percentage of least frequent nodes from the walks at different levels. By this removal, we simulate farther distant nodes to reside in the close neighborhood of a node and hence explicitly represent their connection. Besides the common evaluation tasks for graph embeddings, such as node classification and link prediction, we evaluate and compare our approach against related methods on shortest path approximation. The results indicate, that extensions to random walk based methods (including our own) improve the predictive performance only slightly - if at all.

We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where the observed data are estimated effect sizes from regressions on multiple factors, where the target is the distribution of the true effect sizes. We exploit the fact that any symmetric and unimodal density can be expressed as a mixture of symmetric uniform densities, and model the mixing density in a new way using a Dirichlet process location-mixture of Gamma distributions. We do the computations within a Bayesian context, describe a simple scalable implementation that is linear in the sample size, and show that the estimate of the unknown target density is consistent. Within our application context of regression effect sizes, the target density is likely to have a large probability near zero (the near null effects) coupled with a heavy-tailed distribution (the actual effects). Simulations show that unlike standard deconvolution methods, our Constrained Bayesian Deconvolution method does a much better job of reconstruction of the target density. Applications to a genome-wise association study (GWAS) and microarray data reveal similar results.

We consider combinatorial semi-bandits over a set of arms ${\cal X} \subset \{0,1\}^d$ where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound $R(T) = {\cal O}\Big( {d (\ln m)^2 (\ln T) \over \Delta_{\min} }\Big)$, but it has computational complexity ${\cal O}(|{\cal X}|)$ which is typically exponential in $d$, and cannot be used in large dimensions. We propose the first algorithm which is both computationally and statistically efficient for this problem with regret $R(T) = {\cal O} \Big({d (\ln m)^2 (\ln T)\over \Delta_{\min} }\Big)$ and computational complexity ${\cal O}(T {\bf poly}(d))$. Our approach involves carefully designing an approximate version of ESCB with the same regret guarantees, showing that this approximate algorithm can be implemented in time ${\cal O}(T {\bf poly}(d))$ by repeatedly maximizing a linear function over ${\cal X}$ subject to a linear budget constraint, and showing how to solve this maximization problems efficiently.

We introduce a novel approach to optimize the architecture of deep neural networks by identifying critical neurons and removing non-critical ones. The proposed approach utilizes a mixed integer programming (MIP) formulation of neural models which includes a continuous importance score computed for each neuron in the network. The optimization in MIP solver minimizes the number of critical neurons (i.e., with high importance score) that need to be kept for maintaining the overall accuracy of the model. Further, the proposed formulation generalizes the recently considered lottery ticket optimization by identifying multiple "lucky" sub-networks resulting in optimized architecture that not only perform well on a single dataset, but also generalize across multiple ones upon retraining of network weights. Finally, the proposed framework provides significant improvement in scalability of automatic sparsification of deep network architectures compared to previous attempts. We validate the performance and generalizability of our approach on MNIST, Fashion-MNIST, and CIFAR-10 datasets, using three different neural networks: LeNet 5 and two ReLU fully connected models.

A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and connections to various areas (e.g. Plug-Pichler - stochastic programming, Hellwig - game theory, Aldous - stability of optimal stopping, Hoover-Keisler - model theory). Remarkably, all these seemingly independent approaches define the same adapted weak topology in finite discrete time. Our first main result is to construct an adapted variant of the empirical measure that consistently estimates the laws of stochastic processes in full generality. A natural compatible metric for the weak adapted topology is the given by an adapted refinement of the Wasserstein distance, as established in the seminal works of Pflug-Pichler. Specifically, the adapted Wasserstein distance allows to control the error in stochastic optimization problems, pricing and hedging problems, optimal stopping problems, etc. in a Lipschitz fashion. The second main result of this article yields quantitative bounds for the convergence of the adapted empirical measure with respect to adapted Wasserstein distance. Surprisingly, we obtain virtually the same optimal rates and concentration results that are known for the classical empirical measure wrt. Wasserstein distance.

In recent years, deep learning has become a part of our everyday life and is revolutionizing quantum chemistry as well. In this work, we show how deep learning can be used to advance the research field of photochemistry by learning all important properties for photodynamics simulations. The properties are multiple energies, forces, nonadiabatic couplings and spin-orbit couplings. The nonadiabatic couplings are learned in a phase-free manner as derivatives of a virtually constructed property by the deep learning model, which guarantees rotational covariance. Additionally, an approximation for nonadiabatic couplings is introduced, based on the potentials, their gradients and Hessians. As deep-learning method, we employ SchNet extended for multiple electronic states. In combination with the molecular dynamics program SHARC, our approach termed SchNarc is tested on a model system and two realistic polyatomic molecules and paves the way towards efficient photodynamics simulations of complex systems.

Since its debut in the 18th century, the $\textit{P}$-value has been an integral part of hypothesis testing based scientific discoveries. As the statistical engine ages, questions are beginning to be raised, asking to what extent scientific discoveries based on a $\textit{P}$-value ($\textit{e.g.}$, the practice of drawing scientific conclusions relying on the fact that the $\textit{P}$-value is smaller than an artificially determined threshold, for example, that of 0.05) are reliable and reproducible, and the voice calling for adjusting the significance level of 0.05 or banning the $\textit{P}$-value has been increasingly heard. Inspired by these questions, we inquire into the useful roles and misuses of the $\textit{P}$-value in scientific studies. We attempt to unravel the associations between the $\textit{P}$-value, sample size, significance level, and statistical power. For common misuses and misinterpretations of the $\textit{P}$-value, we provide modest recommendations for practitioners. Additionally, we review, with a comparison, Bayesian alternatives to the $\textit{P}$-value, and discuss the advantages of meta-analysis in combining information, reducing bias, and delivering reproducible evidence. Taken together, we argue that the $\textit{P}$-value underpins a useful probabilistic decision-making system, provides evidence at a continuous scale, and allows for integrating results from multiple studies and data sets. But the interpretation must be contextual, taking into account the scientific question, experimental design (including the sample size and significance level), statistical power, effect size, and reproducibility.

We present a novel attention-based sequential model for mutually dependent spatio-temporal discrete event data, which is a versatile framework for capturing the non-homogeneous influence of events. We go beyond the assumption that the influence of the historical event (causing an upper-ward or downward jump in the intensity function) will fade monotonically over time, which is a key assumption made by many widely-used point process models, including those based on Recurrent Neural Networks (RNNs). We borrow the idea from the attention model based on a probabilistic score function, which leads to a flexible representation of the intensity function and is highly interpretable. We demonstrate the superior performance of our approach compared to the state-of-the-art for both synthetic and real data.

Algorithms that tackle deep exploration -- an important challenge in reinforcement learning -- have relied on epistemic uncertainty representation through ensembles or other hypermodels, exploration bonuses, or visitation count distributions. An open question is whether deep exploration can be achieved by an incremental reinforcement learning algorithm that tracks a single point estimate, without additional complexity required to account for epistemic uncertainty. We answer this question in the affirmative. In particular, we develop Langevin DQN, a variation of DQN that differs only in perturbing parameter updates with Gaussian noise, and demonstrate through a computational study that the algorithm achieves deep exploration. We also provide an intuition for why Langevin DQN performs deep exploration.

We study convex empirical risk minimization for high-dimensional inference in binary models. Our first result sharply predicts the statistical performance of such estimators in the linear asymptotic regime under isotropic Gaussian features. Importantly, the predictions hold for a wide class of convex loss functions, which we exploit in order to prove a bound on the best achievable performance among them. Notably, we show that the proposed bound is tight for popular binary models (such as Signed, Logistic or Probit), by constructing appropriate loss functions that achieve it. More interestingly, for binary linear classification under the Logistic and Probit models, we prove that the performance of least-squares is no worse than 0.997 and 0.98 times the optimal one. Numerical simulations corroborate our theoretical findings and suggest they are accurate even for relatively small problem dimensions.

We consider the estimation of treatment effects in settings when multiple treatments are assigned over time and treatments can have a causal effect on future outcomes. We formulate the problem as a linear state space Markov process with a high dimensional state and propose an extension of the double/debiased machine learning framework to estimate the dynamic effects of treatments. Our method allows the use of arbitrary machine learning methods to control for the high dimensional state, subject to a mean square error guarantee, while still allowing parametric estimation and construction of confidence intervals for the dynamic treatment effect parameters of interest. Our method is based on a sequential regression peeling process, which we show can be equivalently interpreted as a Neyman orthogonal moment estimator. This allows us to show root-n asymptotic normality of the estimated causal effects.

We develop two new stochastic Gauss-Newton algorithms for solving a class of stochastic nonconvex compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard assumptions. We use both classical stochastic and SARAH estimators for approximating function values and Jacobians. In the expectation case, we establish $\mathcal{O}(\varepsilon^{-2})$ iteration complexity to achieve a stationary point in expectation and estimate the total number of stochastic oracle calls for both function values and its Jacobian, where $\varepsilon$ is a desired accuracy. In the finite sum case, we also estimate the same iteration complexity and the total oracle calls with high probability. To our best knowledge, this is the first time such global stochastic oracle complexity is established for stochastic Gauss-Newton methods. We illustrate our theoretical results via numerical examples on both synthetic and real datasets.

We study the problem of estimating the distribution of effect sizes (the mean of the test statistic under the alternate hypothesis) in a multiple testing setting. Knowing this distribution allows us to calculate the power (type II error) of any experimental design. We show that it is possible to estimate this distribution using an inexpensive pilot experiment, which takes significantly fewer samples than would be required by an experiment that identified the discoveries. Our estimator can be used to guarantee the number of discoveries that will be made using a given experimental design in a future experiment. We prove that this simple and computationally efficient estimator enjoys a number of favorable theoretical properties, and demonstrate its effectiveness on data from a gene knockout experiment on influenza inhibition in Drosophila.

In general, adversarial perturbations superimposed on inputs are realistic threats for a deep neural network (DNN). In this paper, we propose a practical generation method of such adversarial perturbation to be applied to black-box attacks that demand access to an input-output relationship only. Thus, the attackers generate such perturbation without invoking inner functions and/or accessing the inner states of a DNN. Unlike the earlier studies, the algorithm to generate the perturbation presented in this study requires much fewer query trials. Moreover, to show the effectiveness of the adversarial perturbation extracted, we experiment with a DNN for semantic segmentation. The result shows that the network is easily deceived with the perturbation generated than using uniformly distributed random noise with the same magnitude.

It is commonly observed that the data are scattered everywhere and difficult to be centralized. The data privacy and security also become a sensitive topic. The laws and regulations such as the European Union's General Data Protection Regulation (GDPR) are designed to protect the public's data privacy. However, machine learning requires a large amount of data for better performance, and the current circumstances put deploying real-life AI applications in an extremely difficult situation. To tackle these challenges, in this paper we propose a novel privacy-preserving federated machine learning model, named Federated Extra-Trees, which applies local differential privacy in the federated trees model. A secure multi-institutional machine learning system was developed to provide superior performance by processing the modeling jointly on different clients without exchanging any raw data. We have validated the accuracy of our work by conducting extensive experiments on public datasets and the efficiency and robustness were also verified by simulating the real-world scenarios. Overall, we presented an extensible, scalable and practical solution to handle the data island problem.

A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian random noise. Then, the stability of posterior is studied for observation data. For each point of the space, the conditional probability that the point is included in the unknown domain given the observation data is considered. The stability is also studied for this probability distribution. As a model problem for our inverse problem, a heat inverse problem is considered. This problem requires the determination of the unknown shape of cavities in a heat conductor from temperature data of some portion of the surface of the heat conductor. To apply the above stability results to this model problem, one needs the measurability and some boundedness of the forward operator. These properties are shown.

Area under ROC curve (AUC) is a widely used performance measure for classification models. We propose a new distributionally robust AUC maximization model (DR-AUC) that relies on the Kantorovich metric and approximates the AUC with the hinge loss function. We use duality theory to reformulate the DR-AUC model as a tractable convex quadratic optimization problem. The numerical experiments show that the proposed DR-AUC model -- benchmarked with the standard deterministic AUC and the support vector machine models - improves the out-of-sample performance over the majority of the considered datasets. The results are particularly encouraging since our numerical experiments are conducted with training sets of small size which have been known to be conducive to low out-of-sample performance.

We present a new active learning algorithm that adaptively partitions the input space into a finite number of regions, and subsequently seeks a distinct predictor for each region, both phases actively requesting labels. We prove theoretical guarantees for both the generalization error and the label complexity of our algorithm, and analyze the number of regions defined by the algorithm under some mild assumptions. We also report the results of an extensive suite of experiments on several real-world datasets demonstrating substantial empirical benefits over existing single-region and non-adaptive region-based active learning baselines.

Unsupervised anomaly detection aims to identify anomalous samples from highly complex and unstructured data, which is pervasive in both fundamental research and industrial applications. However, most existing methods neglect the complex correlation among data samples, which is important for capturing normal patterns from which the abnormal ones deviate. In this paper, we propose a method of Correlation aware unsupervised Anomaly detection via Deep Gaussian Mixture Model (CADGMM), which captures the complex correlation among data points for high-quality low-dimensional representation learning. Specifically, the relations among data samples are correlated firstly in forms of a graph structure, in which, the node denotes the sample and the edge denotes the correlation between two samples from the feature space. Then, a dual-encoder that consists of a graph encoder and a feature encoder, is employed to encode both the feature and correlation information of samples into the low-dimensional latent space jointly, followed by a decoder for data reconstruction. Finally, a separate estimation network as a Gaussian Mixture Model is utilized to estimate the density of the learned latent vector, and the anomalies can be detected by measuring the energy of the samples. Extensive experiments on real-world datasets demonstrate the effectiveness of the proposed method.

Sliced-Wasserstein distance (SWD) and its variation, Max Sliced-Wasserstein distance (Max-SWD), have been widely used in the recent years due to their fast computation and scalability when the probability measures lie in very high dimension. However, these distances still have their weakness, SWD requires a lot of projection samples because it uses the uniform distribution to sample projecting directions, Max-SWD uses only one projection, causing it to lose a large amount of information. In this paper, we propose a novel distance that finds optimal penalized probability measure over the slices, which is named Distributional Sliced-Wasserstein distance (DSWD). We show that the DSWD is a generalization of both SWD and Max-SWD, and the proposed distance could be found by searching for the push-forward measure over a set of measures satisfying some certain constraints. Moreover, similar to SWD, we can extend Generalized Sliced-Wasserstein distance (GSWD) to Distributional Generalized Sliced-Wasserstein distance (DGSWD). Finally, we carry out extensive experiments to demonstrate the favorable generative modeling performances of our distances over the previous sliced-based distances in large-scale real datasets.

Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. In this work, we study high-dimensional varying-coefficient quantile regression model that allows us to capture non-stationary effects of the input variables across time. We develop new tools for statistical inference that allow us to construct valid confidence intervals and honest tests for nonparametric coefficient at fixed time and quantile. Our focus is on inference in a high-dimensional setting where the number of input variables exceeds the sample size. Performing statistical inference in this regime is challenging due to the usage of model selection techniques in estimation. Never the less, we are able to develop valid inferential tools that are applicable to a wide range of data generating processes and do not suffer from biases introduced by model selection. The statistical framework allows us to construct a confidence interval at a fixed point in time and a fixed quantile based on a Normal approximation. We performed numerical simulations to demonstrate the finite sample performance of our method and we also illustrated the application with a real data example.

A Relational Markov Decision Process (RMDP) is a first-order representation to express all instances of a single probabilistic planning domain with possibly unbounded number of objects. Early work in RMDPs outputs generalized (instance-independent) first-order policies or value functions as a means to solve all instances of a domain at once. Unfortunately, this line of work met with limited success due to inherent limitations of the representation space used in such policies or value functions. Can neural models provide the missing link by easily representing more complex generalized policies, thus making them effective on all instances of a given domain?

We present the first neural approach for solving RMDPs, expressed in the probabilistic planning language of RDDL. Our solution first converts an RDDL instance into a ground DBN. We then extract a graph structure from the DBN. We train a relational neural model that computes an embedding for each node in the graph and also scores each ground action as a function over the first-order action variable and object embeddings on which the action is applied. In essence, this represents a neural generalized policy for the whole domain. Given a new test problem of the same domain, we can compute all node embeddings using trained parameters and score each ground action to choose the best action using a single forward pass without any retraining. Our experiments on nine RDDL domains from IPPC demonstrate that neural generalized policies are significantly better than random and sometimes even more effective than training a state-of-the-art deep reactive policy from scratch.

Overparameterization has been shown to benefit both the optimization and generalization of neural networks, but large networks are resource hungry at both training and test time. Network pruning can reduce test-time resource requirements, but is typically applied to trained networks and therefore cannot avoid the expensive training process. We aim to prune networks at initialization, thereby saving resources at training time as well. Specifically, we argue that efficient training requires preserving the gradient flow through the network. This leads to a simple but effective pruning criterion we term Gradient Signal Preservation (GraSP). We empirically investigate the effectiveness of the proposed method with extensive experiments on CIFAR-10, CIFAR-100, Tiny-ImageNet and ImageNet, using VGGNet and ResNet architectures. Our method can prune 80% of the weights of a VGG-16 network on ImageNet at initialization, with only a 1.6% drop in top-1 accuracy. Moreover, our method achieves significantly better performance than the baseline at extreme sparsity levels.

Self-supervision is key to extending use of deep learning for label scarce domains. For most of self-supervised approaches data transformations play an important role. However, up until now the impact of transformations have not been studied. Furthermore, different transformations may have different impact on the system. We provide novel insights into the use of data transformation in self-supervised tasks, specially pertaining to clustering. We show theoretically and empirically that certain set of transformations are helpful in convergence of self-supervised clustering. We also show the cases when the transformations are not helpful or in some cases even harmful. We show faster convergence rate with valid transformations for convex as well as certain family of non-convex objectives along with the proof of convergence to the original set of optima. We have synthetic as well as real world data experiments. Empirically our results conform with the theoretical insights provided.

When a neural network is partitioned and distributed across physical nodes, failure of physical nodes causes the failure of the neural units that are placed on those nodes, which results in a significant performance drop. Current approaches focus on resiliency of training in distributed neural networks. However, resiliency of inference in distributed neural networks is less explored. We introduce ResiliNet, a scheme for making inference in distributed neural networks resilient to physical node failures. ResiliNet combines two concepts to provide resiliency: skip connection in residual neural networks, and a novel technique called failout, which is introduced in this paper. Failout simulates physical node failure conditions during training using dropout, and is specifically designed to improve the resiliency of distributed neural networks. The results of the experiments and ablation studies using three datasets confirm the ability of ResiliNet to provide inference resiliency for distributed neural networks.

Modern quantitative risk management relies on an adequate modeling of the tail dependence and a possibly accurate quantification of risk measures, like Value at Risk (VaR), at high confidence levels like 1 in 100 or even 1 in 2000. Quantum computing makes such a quantification quadratically more efficient than the Monte Carlo method; see (Woerner and Egger, 2018) and, for a broader perspective, (Or\'us et al., 2018). An important element of the risk analysis toolbox is copula, see (Jouanin et al., 2004) regarding financial applications. However, to the best knowledge of the author, no quantum computing implementation for sampling from a risk modeling-relevant copula in explicit form has been published so far. Our focus here is implementation of simple yet powerful copula models, capable of a satisfactory capturing the joint tail behaviour of the modelled risk factors. This paper deals with a few simple copula families, including Multivariate B11 (MB11) copula family, presented in (Milek, 2014). We will show that this copula family is suitable for the risk aggregation as it is exceptionally able to reproduce tail dependence structures; see (Embrechts et al., 2016) for a relevant benchmark as well as necessary and sufficient conditions regarding the ultimate feasible bivariate tail dependence structures. It turns out that such a discretized copula can be expressed using simple constructs present in the quantum computing: binary fraction expansion format, comonotone/independent random variables, controlled gates, and convex combinations, and is therefore suitable for a quantum computer implementation. This paper presents design behind the quantum implementation circuits, numerical and symbolic simulation results, and experimental validation on IBM quantum computer. The paper proposes also a generic method for quantum implementation of any discretized copula.

Federated learning is a new distributed machine learning framework, where a bunch of heterogeneous clients collaboratively train a model without sharing training data. In this work, we consider a practical and ubiquitous issue in federated learning: intermittent client availability, where the set of eligible clients may change during the training process. Such an intermittent client availability model would significantly deteriorate the performance of the classical Federated Averaging algorithm (FedAvg for short). We propose a simple distributed non-convex optimization algorithm, called Federated Latest Averaging (FedLaAvg for short), which leverages the latest gradients of all clients, even when the clients are not available, to jointly update the global model in each iteration. Our theoretical analysis shows that FedLaAvg attains the convergence rate of $O(1/(N^{1/4} T^{1/2}))$, achieving a sublinear speedup with respect to the total number of clients. We implement and evaluate FedLaAvg with the CIFAR-10 dataset. The evaluation results demonstrate that FedLaAvg indeed reaches a sublinear speedup and achieves 4.23% higher test accuracy than FedAvg.

In recent years we see a rapidly growing line of research which shows learnability of various models via common neural network algorithms. Yet, besides a very few outliers, these results show learnability of models that can be learned using linear methods. Namely, such results show that learning neural-networks with gradient-descent is competitive with learning a linear classifier on top of a data-independent representation of the examples. This leaves much to be desired, as neural networks are far more successful than linear methods. Furthermore, on the more conceptual level, linear models don't seem to capture the deepness" of deep networks. In this paper we make a step towards showing leanability of models that are inherently non-linear. We show that under certain distributions, sparse parities are learnable via gradient decent on depth-two network. On the other hand, under the same distributions, these parities cannot be learned efficiently by linear methods.

There has been an ongoing cycle where stronger defenses against adversarial attacks are subsequently broken by a more advanced defense-aware attack. We present a new approach towards ending this cycle where we "deflect'' adversarial attacks by causing the attacker to produce an input that semantically resembles the attack's target class. To this end, we first propose a stronger defense based on Capsule Networks that combines three detection mechanisms to achieve state-of-the-art detection performance on both standard and defense-aware attacks. We then show that undetected attacks against our defense often perceptually resemble the adversarial target class by performing a human study where participants are asked to label images produced by the attack. These attack images can no longer be called "adversarial'' because our network classifies them the same way as humans do.

Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are (Pseudo-)Riemannian metrices, which in the category of statistical models are induced by statistical divergences. The present article is intended to extend the notation of topological statistical models by a differential structure to statistical manifolds and to introduce the differential geometric foundations to study specific families of probability distributions. In this purpose the article successively incorporates the structures of differential-, Riemannian- and symplectic geometry within an underlying topological statistical model. The last section addresses a specific structural category, termed a dually flat statistical manifold, which can be used to study the properties of exponential families, which are of particular importance in machine learning and deep learning.

In this paper, we aim to give a theoretical approximation for the penalty level of $\ell_{1}$-regularization problems. This can save much time in practice compared with the traditional methods, such as cross-validation. To achieve this goal, we develop two Gaussian approximation methods, which are based on a moderate deviation theorem and Stein's method respectively. Both of them give efficient approximations and have good performances in simulations. We apply the two Gaussian approximation methods into three types of ultra-high dimensional $\ell_{1}$ penalized regressions: lasso, square-root lasso, and weighted $\ell_{1}$ penalized Poisson regression. The numerical results indicate that our two ways to estimate the penalty levels achieve high computational efficiency. Besides, our prediction errors outperform that based on the 10-fold cross-validation.

We prove the consistency of the $\ell_1$ penalized negative binomial regression (NBR). A real data application about German health care demand shows that the $\ell_1$ penalized NBR produces a more concise but more accurate model, comparing to the classical NBR.

We consider practical data characteristics underlying federated learning, where unbalanced and non-i.i.d. data from clients have a block-cyclic structure: each cycle contains several blocks, and each client's training data follow block-specific and non-i.i.d. distributions. Such a data structure would introduce client and block biases during the collaborative training: the single global model would be biased towards the client or block specific data. To overcome the biases, we propose two new distributed optimization algorithms called multi-model parallel SGD (MM-PSGD) and multi-chain parallel SGD (MC-PSGD) with a convergence rate of $O(1/\sqrt{NT})$, achieving a linear speedup with respect to the total number of clients. In particular, MM-PSGD adopts the block-mixed training strategy, while MC-PSGD further adds the block-separate training strategy. Both algorithms create a specific predictor for each block by averaging and comparing the historical global models generated in this block from different cycles. We extensively evaluate our algorithms over the CIFAR-10 dataset. Evaluation results demonstrate that our algorithms significantly outperform the conventional federated averaging algorithm in terms of test accuracy, and also preserve robustness for the variance of critical parameters.

Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional neural networks (CNNs). Common GMRFs are special cases of a generative model where the inverse mapping from data to latent variables is given by a 1-layer linear CNN. This connection allows us to generalize GMRFs to multi-layer CNN architectures, effectively increasing the order of the corresponding GMRF in a way which has favorable computational scaling. We describe how well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the deep GMRF. We demonstrate the flexibility of the proposed model and show that it outperforms the state-of-the-art on a dataset of satellite temperatures, in terms of prediction and predictive uncertainty.

In this paper, a Neural network is derived from first principles, assuming only that each layer begins with a linear dimension-reducing transformation. The approach appeals to the principle of Maximum Entropy (MaxEnt) to find the posterior distribution of the input data of each layer, conditioned on the layer output variables. This posterior has a well-defined mean, the conditional mean estimator, that is calculated using a type of neural network with theoretically-derived activation functions similar to sigmoid, softplus, and relu. This implicitly provides a theoretical justification for their use. A theorem that finds the conditional distribution and conditional mean estimator under the MaxEnt prior is proposed, unifying results for special cases. Combining layers results in an auto-encoder with conventional feed-forward analysis network and a type of linear Bayesian belief network in the reconstruction path.

It is often useful to tap secondary information from a running R script. Obvious use cases include logging, and profiling of time or memory consuption. Perhaps less obvious cases include tracking changes in R objects or collecting output of unit tests (assertions). In this paper we demonstrate an approach that abstracts collection and processing of such secondary information from the code in the running script. The approach is implemented in pure R, and allows users to control the secondary information stream stream without global side effects and without altering existing code. Although some elements of the approach discussed here have been applied in existing packages, the combination of elements proposed here appears thus far to have been overlooked.

We designed a machine learning algorithm that identifies patterns between ESG profiles and financial performances for companies in a large investment universe. The algorithm consists of regularly updated sets of rules that map regions into the high-dimensional space of ESG features to excess return predictions. The final aggregated predictions are transformed into scores which allow us to design simple strategies that screen the investment universe for stocks with positive scores. By linking the ESG features with financial performances in a non-linear way, our strategy based upon our machine learning algorithm turns out to be an efficient stock picking tool, which outperforms classic strategies that screen stocks according to their ESG ratings, as the popular best-in-class approach. Our paper brings new ideas in the growing field of financial literature that investigates the links between ESG behavior and the economy. We show indeed that there is clearly some form of alpha in the ESG profile of a company, but that this alpha can be accessed only with powerful, non-linear techniques such as machine learning.

Land-use regression (LUR) models are important for the assessment of air pollution concentrations in areas without measurement stations. While many such models exist, they often use manually constructed features based on restricted, locally available data. Thus, they are typically hard to reproduce and challenging to adapt to areas beyond those they have been developed for. In this paper, we advocate a paradigm shift for LUR models: We propose the Data-driven, Open, Global (DOG) paradigm that entails models based on purely data-driven approaches using only openly and globally available data. Progress within this paradigm will alleviate the need for experts to adapt models to the local characteristics of the available data sources and thus facilitate the generalizability of air pollution models to new areas on a global scale. In order to illustrate the feasibility of the DOG paradigm for LUR, we introduce a deep learning model called MapLUR. It is based on a convolutional neural network architecture and is trained exclusively on globally and openly available map data without requiring manual feature engineering. We compare our model to state-of-the-art baselines like linear regression, random forests and multi-layer perceptrons using a large data set of modeled $\text{NO}_2$ concentrations in Central London. Our results show that MapLUR significantly outperforms these approaches even though they are provided with manually tailored features. Furthermore, we illustrate that the automatic feature extraction inherent to models based on the DOG paradigm can learn features that are readily interpretable and closely resemble those commonly used in traditional LUR approaches.

Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family of learning objectives including score matching, by observing a new connection between these objectives and Wasserstein gradient flows. We present applications with promise in learning neural density estimators on manifolds, and training implicit variational and Wasserstein auto-encoders with a manifold-valued prior.

Graph neural networks (GNNs) have received much attention recently because of their excellent performance on graph-based tasks. However, existing research on GNNs focuses on designing more effective models without considering much the quality of the input data itself. In this paper, we propose self-enhanced GNN, which improves the quality of the input data using the outputs of existing GNN models for better performance on semi-supervised node classification. As graph data consist of both topology and node labels, we improve input data quality from both perspectives. For topology, we observe that higher classification accuracy can be achieved when the ratio of inter-class edges (connecting nodes from different classes) is low and propose topology update to remove inter-class edges and add intra-class edges. For node labels, we propose training node augmentation, which enlarges the training set using the labels predicted by existing GNN models. As self-enhanced GNN improves the quality of the input graph data, it is general and can be easily combined with existing GNN models. Experimental results on three well-known GNN models and seven popular datasets show that self-enhanced GNN consistently improves the performance of the three models. The reduction in classification error is 16.2% on average and can be as high as 35.1%.

We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our approach enables storing a single set of weights that can be quantized on-demand to different bit-widths as energy and memory requirements of the application change. Unlike quantization-aware training using the straight-through estimator that only targets a specific bit-width and requires access to training data and pipeline, our regularization-based method paves the way for "on the fly'' post-training quantization to various bit-widths. We show that by modeling quantization as a $\ell_\infty$-bounded perturbation, the first-order term in the loss expansion can be regularized using the $\ell_1$-norm of gradients. We experimentally validate the effectiveness of our regularization scheme on different architectures on CIFAR-10 and ImageNet datasets.

We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element of the proposed network architecture is a new $G$-invariant transformation module, which produces a $G$-invariant latent representation of the input data. This latent representation is then processed with a multi-layer perceptron in the network. We prove the universality of the proposed architecture, discuss its properties and highlight its computational and memory efficiency. Theoretical considerations are supported by numerical experiments involving different network configurations, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other $G$-invariant neural networks.

The generalized linear bandit framework has attracted a lot of attention in recent years by extending the well-understood linear setting and allowing to model richer reward structures. It notably covers the logistic model, widely used when rewards are binary. For logistic bandits, the frequentist regret guarantees of existing algorithms are $\tilde{\mathcal{O}}(\kappa \sqrt{T})$, where $\kappa$ is a problem-dependent constant. Unfortunately, $\kappa$ can be arbitrarily large as it scales exponentially with the size of the decision set. This may lead to significantly loose regret bounds and poor empirical performance. In this work, we study the logistic bandit with a focus on the prohibitive dependencies introduced by $\kappa$. We propose a new optimistic algorithm based on a finer examination of the non-linearities of the reward function. We show that it enjoys a $\tilde{\mathcal{O}}(\sqrt{T})$ regret with no dependency in $\kappa$, but for a second order term. Our analysis is based on a new tail-inequality for self-normalized martingales, of independent interest.

We consider two agents playing simultaneously the same stochastic three-armed bandit problem. The two agents are cooperating but they cannot communicate. We propose a strategy with no collisions at all between the players (with very high probability), and with near-optimal regret $O(\sqrt{T \log(T)})$. We also provide evidence that the extra logarithmic term $\sqrt{\log(T)}$ is necessary, with a lower bound for a variant of the problem.

Systematic reviews aim to summarize all the available evidence relevant to a particular research question. If appropriate, the data from identified studies are quantitatively combined in a meta-analysis. Often only few studies regarding a particular research question exist. In these settings the estimation of the between-study heterogeneity is challenging. Furthermore, the assessment of publication bias is difficult as standard methods such as visual inspection or formal hypothesis tests in funnel plots do not provide adequate guidance. Previously, Henmi and Copas (Statistics in Medicine 2010, 29: 2969-2983) proposed a confidence interval for the overall effect in random-effects meta-analysis that is robust to publication bias to some extent. As is evident from their simulations, the confidence intervals have improved coverage compared with standard methods. To our knowledge, the properties of their method has never been assessed for meta-analyses including fewer than five studies. In this manuscript, we propose a variation of the method by Henmi and Copas employing an improved estimator of the between-study heterogeneity, in particular when dealing with few studies only. In a simulation study, the proposed method is compared to several competitors. Overall, we found that our method outperforms the others in terms. In particular, an improvement in coverage probability of the new method compared with the proposal by Henmi and Copas is demonstrated. The work is motivated and illustrated by a systematic review and meta-analysis in paediatric immunosuppression following liver transplantations.

Inspired by the recent advances in deep learning (DL), this work presents a deep neural network aided decoding algorithm for binary linear codes. Based on the concept of deep unfolding, we design a decoding network by unfolding the alternating direction method of multipliers (ADMM)-penalized decoder. In addition, we propose two improved versions of the proposed network. The first one transforms the penalty parameter into a set of iteration-dependent ones, and the second one adopts a specially designed penalty function, which is based on a piecewise linear function with adjustable slopes. Numerical results show that the resulting DL-aided decoders outperform the original ADMM-penalized decoder for various low density parity check (LDPC) codes with similar computational complexity.

With the rapid development of manufacturing industry, machine fault diagnosis has become increasingly significant to ensure safe equipment operation and production. Consequently, multifarious approaches have been explored and developed in the past years, of which intelligent algorithms develop particularly rapidly. Convolutional neural network, as a typical representative of intelligent diagnostic models, has been extensively studied and applied in recent five years, and a large amount of literature has been published in academic journals and conference proceedings. However, there has not been a systematic review to cover these studies and make a prospect for the further research. To fill in this gap, this work attempts to review and summarize the development of the Convolutional Network based Fault Diagnosis (CNFD) approaches comprehensively. Generally, a typical CNFD framework is composed of the following steps, namely, data collection, model construction, and feature learning and decision making, thus this paper is organized by following this stream. Firstly, data collection process is described, in which several popular datasets are introduced. Then, the fundamental theory from the basic convolutional neural network to its variants is elaborated. After that, the applications of CNFD are reviewed in terms of three mainstream directions, i.e. classification, prediction and transfer diagnosis. Finally, conclusions and prospects are presented to point out the characteristics of current development, facing challenges and future trends. Last but not least, it is expected that this work would provide convenience and inspire further exploration for researchers in this field.

Medical images differ from natural images in significantly higher resolutions and smaller regions of interest. Because of these differences, neural network architectures that work well for natural images might not be applicable to medical image analysis. In this work, we extend the globally-aware multiple instance classifier, a framework we proposed to address these unique properties of medical images. This model first uses a low-capacity, yet memory-efficient, network on the whole image to identify the most informative regions. It then applies another higher-capacity network to collect details from chosen regions. Finally, it employs a fusion module that aggregates global and local information to make a final prediction. While existing methods often require lesion segmentation during training, our model is trained with only image-level labels and can generate pixel-level saliency maps indicating possible malignant findings. We apply the model to screening mammography interpretation: predicting the presence or absence of benign and malignant lesions. On the NYU Breast Cancer Screening Dataset, consisting of more than one million images, our model achieves an AUC of 0.93 in classifying breasts with malignant findings, outperforming ResNet-34 and Faster R-CNN. Compared to ResNet-34, our model is 4.1x faster for inference while using 78.4% less GPU memory. Furthermore, we demonstrate, in a reader study, that our model surpasses radiologist-level AUC by a margin of 0.11. The proposed model is available online: https://github.com/nyukat/GMIC.

Although freelancing work has grown substantially in recent years, in part facilitated by a number of online labor marketplaces, (e.g., Guru, Freelancer, Amazon Mechanical Turk), traditional forms of "in-sourcing" work continue being the dominant form of employment. This means that, at least for the time being, freelancing and salaried employment will continue to co-exist. In this paper, we provide algorithms for outsourcing and hiring workers in a general setting, where workers form a team and contribute different skills to perform a task. We call this model team formation with outsourcing. In our model, tasks arrive in an online fashion: neither the number nor the composition of the tasks is known a-priori. At any point in time, there is a team of hired workers who receive a fixed salary independently of the work they perform. This team is dynamic: new members can be hired and existing members can be fired, at some cost. Additionally, some parts of the arriving tasks can be outsourced and thus completed by non-team members, at a premium. Our contribution is an efficient online cost-minimizing algorithm for hiring and firing team members and outsourcing tasks. We present theoretical bounds obtained using a primal-dual scheme proving that our algorithms have a logarithmic competitive approximation ratio. We complement these results with experiments using semi-synthetic datasets based on actual task requirements and worker skills from three large online labor marketplaces.

In the inverse Gaussian sequence space model with additional noisy observations of the operator, we derive nonasymptotic minimax radii of testing for ellipsoid-type alternatives simultaneously for both the signal detection problem (testing against zero) and the goodness-of-fit testing problem (testing against a prescribed sequence) without any regularity assumption on the null hypothesis. The radii are the maximum of two terms, each of which only depends on one of the noise levels. Interestingly, the term involving the noise level of the operator explicitly depends on the null hypothesis and vanishes in the signal detection case. The minimax radii are established by first showing a lower bound for arbitrary null hypotheses and noise levels. For the upper bound we consider two testing procedures, a direct test based on estimating the energy in the image space and an indirect test. Under mild assumptions, we prove that the testing radius of the indirect test achieves the lower bound, which shows the minimax optimality of the radius and the test. We highlight the assumptions under which the direct test also performs optimally. Furthermore, we apply a classical Bonferroni method for making both the indirect and the direct test adaptive with respect to the regularity of the alternative. The radii of the adaptive tests are deteriorated by an additional log-factor, which we show to be unavoidable. The results are illustrated considering Sobolev spaces and mildly or severely ill-posed inverse problems.

Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general structured principal subspace estimation problem which includes as special cases non-negative PCA/SVD, sparse PCA/SVD, subspace constrained PCA/SVD, and spectral clustering. General minimax lower and upper bounds are established to characterize the interplay between the information-geometric complexity of the structural set for the principal subspaces, the signal-to-noise ratio (SNR), and the dimensionality. The results yield interesting phase transition phenomena concerning the rates of convergence as a function of the SNRs and the fundamental limit for consistent estimation. Applying the general results to the specific settings yields the minimax rates of convergence for those problems, including the previous unknown optimal rates for non-negative PCA/SVD, sparse SVD and subspace constrained PCA/SVD.

Automatic speaker verification systems are vulnerable to audio replay attacks which bypass security by replaying recordings of authorized speakers. Replay attack detection (RA) detection systems built upon Residual Neural Networks (ResNet)s have yielded astonishing results on the public benchmark ASVspoof 2019 Physical Access challenge. With most teams using fine-tuned feature extraction pipelines and model architectures, the generalizability of such systems remains questionable though. In this work, we analyse the effect of discriminative feature learning in a multi-task learning (MTL) setting can have on the generalizability and discriminability of RA detection systems. We use a popular ResNet architecture optimized by the cross-entropy criterion as our baseline and compare it to the same architecture optimized by MTL using Siamese Neural Networks (SNN). It can be shown that SNN outperform the baseline by relative 26.8 % Equal Error Rate (EER). We further enhance the model's architecture and demonstrate that SNN with additional reconstruction loss yield another significant improvement of relative 13.8 % EER.

We consider the problem of downlink power control in wireless networks, consisting of multiple transmitter-receiver pairs communicating with each other over a single shared wireless medium. To mitigate the interference among concurrent transmissions, we leverage the network topology to create a graph neural network architecture, and we then use an unsupervised primal-dual counterfactual optimization approach to learn optimal power allocation decisions. We show how the counterfactual optimization technique allows us to guarantee a minimum rate constraint, which adapts to the network size, hence achieving the right balance between average and $5^{th}$ percentile user rates throughout a range of network configurations.

We present a method for financial time series forecasting using representation learning techniques. Recent progress on deep autoregressive models has shown their ability to capture long-term dependencies of the sequence data. However, the shortage of available financial data for training will make the deep models susceptible to the overfitting problem. In this paper, we propose a neural-network-powered conditional mutual information (CMI) estimator for learning representations for the forecasting task. Specifically, we first train an encoder to maximize the mutual information between the latent variables and the label information conditioned on the encoded observed variables. Then the features extracted from the trained encoder are used to learn a subsequent logistic regression model for predicting time series movements. Our proposed estimator transforms the CMI maximization problem to a classification problem whether two encoded representations are sampled from the same class or not. This is equivalent to perform pairwise comparisons of the training datapoints, and thus, improves the generalization ability of the deep autoregressive model. Empirical experiments indicate that our proposed method has the potential to advance the state-of-the-art performance.

Uncertainty estimation is important for ensuring safety and robustness of AI systems, especially for high-risk applications. While much progress has recently been made in this area, most research has focused on un-structured prediction, such as image classification and regression tasks. However, while task-specific forms of confidence score estimation have been investigated by the speech and machine translation communities, limited work has investigated general uncertainty estimation approaches for structured prediction. Thus, this work aims to investigate uncertainty estimation for structured prediction tasks within a single unified and interpretable probabilistic ensemble-based framework. We consider uncertainty estimation for sequence data at the token-level and complete sequence-level, provide interpretations for, and applications of, various measures of uncertainty and discuss the challenges associated with obtaining them. This work also explores the practical challenges associated with obtaining uncertainty estimates for structured predictions tasks and provides baselines for token-level error detection, sequence-level prediction rejection, and sequence-level out-of-domain input detection using ensembles of auto-regressive transformer models trained on the WMT'14 English-French and WMT'17 English-German translation and LibriSpeech speech recognition datasets.

We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space that can be used to induce a transformation from a simple probability distribution to a more complex one: if the simple distribution can be rapidly sampled and its density evaluated, then so can the complex distribution. Our first application to gravitational waves uses an autoregressive flow, conditioned on detector strain data, to map a multivariate standard normal distribution into the posterior distribution over system parameters. We train the model on artificial strain data consisting of IMRPhenomPv2 waveforms drawn from a five-parameter $(m_1, m_2, \phi_0, t_c, d_L)$ prior and stationary Gaussian noise realizations with a fixed power spectral density. This gives performance comparable to current best deep-learning approaches to gravitational-wave parameter estimation. We then build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework. This model has performance comparable to Markov chain Monte Carlo and, in particular, successfully models the multimodal $\phi_0$ posterior. Finally, we train the autoregressive latent variable model on an expanded parameter space, including also aligned spins $(\chi_{1z}, \chi_{2z})$ and binary inclination $\theta_{JN}$, and show that all parameters and degeneracies are well-recovered. In all cases, sampling is extremely fast, requiring less than two seconds to draw $10^4$ posterior samples.

Common reporting styles of statistical results, such as confidence intervals (CI), are prone to dichotomous interpretations especially on null hypothesis testing frameworks, for example by claiming significant differences between drug treatment and placebo groups due to the non-overlapping CIs of the mean effects, while disregarding the magnitudes and absolute difference in the effect sizes. Techniques relying on the visual estimation of the strength of evidence have been recommended to limit such dichotomous interpretations but their effectiveness has been challenged. We ran two experiments to compare several representation alternatives of confidence intervals, and used Bayesian multilevel models to estimate the effects of the representation styles on differences in subjective confidence of the results and preferences in visualization styles. Our results suggest that adding visual information to classic CI representation can decrease the sudden drop around $p$-value 0.05 compared to classic CIs and textual representation of CI with $p$-values. All data analysis and scripts are available at https://github.com/helske/statvis.

In this paper we characterize the performance of a class of maximum-a-posteriori (MAP) detectors for network systems driven by unknown stochastic inputs, as a function of the location of the sensors and the topology of the network. We consider two scenarios: one in which the changes occurs in the mean of the input, and the other where the changes are allowed to happen in the covariance (or power) of the input. In both the scenarios, to detect the changes, we associate suitable MAP detectors for a given set of sensors, and study its detection performance as function of the network topology, and the graphical distance between the input nodes and the sensors location. When the input and measurement noise follow a Gaussian distribution, we show that, as the number of measurements goes to infinity, the detectors' performance can be studied using the input to output gain of the transfer function of the network system. Using this characterization, we derive conditions under which the detection performance obtained when the sensors are located on a network cut is not worse (resp. not better) than the performance obtained by measuring all nodes of the subnetwork induced by the cut and not containing the input nodes. Our results provide structural insights into the sensor placement from a detection-theoretic viewpoint. Finally, we illustrate our findings via numerical examples.

Calibration and equal error rates are fundamental conditions for algorithmic fairness that have been shown to conflict with each other, suggesting that they cannot be satisfied simultaneously. This paper shows that the two are in fact compatible and presents a method for reconciling them. In particular, we derive necessary and sufficient conditions for the existence of calibrated scores that yield classifications achieving equal error rates. We then present an algorithm that searches for the most informative score subject to both calibration and minimal error rate disparity. Applied empirically to credit lending, our algorithm provides a solution that is more fair and profitable than a common alternative that omits sensitive features.

Infrared spectra obtained from cell or tissue specimen have commonly been observed to involve a significant degree of (resonant) Mie scattering, which often overshadows biochemically relevant spectral information by a non-linear, non-additive spectral component in Fourier transformed infrared (FTIR) spectroscopic measurements. Correspondingly, many successful machine learning approaches for FTIR spectra have relied on preprocessing procedures that computationally remove the scattering components from an infrared spectrum. We propose an approach to approximate this complex preprocessing function using deep neural networks. As we demonstrate, the resulting model is not just several orders of magnitudes faster, which is important for real-time clinical applications, but also generalizes strongly across different tissue types. Furthermore, our proposed method overcomes the trade-off between computation time and the corrected spectrum being biased towards an artificial reference spectrum.

Fueled by massive data, important decision making is being automated with the help of algorithms, therefore, fairness in algorithms has become an especially important research topic. In this work, we design new streaming and distributed algorithms for the fair $k$-center problem that models fair data summarization. The streaming and distributed models of computation have an attractive feature of being able to handle massive data sets that do not fit into main memory. Our main contributions are: (a) the first distributed algorithm; which has provably constant approximation ratio and is extremely parallelizable, and (b) a two-pass streaming algorithm with a provable approximation guarantee matching the best known algorithm (which is not a streaming algorithm). Our algorithms have the advantages of being easy to implement in practice, being fast with linear running times, having very small working memory and communication, and outperforming existing algorithms on several real and synthetic data sets. To complement our distributed algorithm, we also give a hardness result for natural distributed algorithms, which holds for even the special case of $k$-center.

In many real world applications, data are characterized by a complex structure, that can be naturally encoded as a graph. In the last years, the popularity of deep learning techniques has renewed the interest in neural models able to process complex patterns. In particular, inspired by the Graph Neural Network (GNN) model, different architectures have been proposed to extend the original GNN scheme. GNNs exploit a set of state variables, each assigned to a graph node, and a diffusion mechanism of the states among neighbor nodes, to implement an iterative procedure to compute the fixed point of the (learnable) state transition function. In this paper, we propose a novel approach to the state computation and the learning algorithm for GNNs, based on a constraint optimisation task solved in the Lagrangian framework. The state convergence procedure is implicitly expressed by the constraint satisfaction mechanism and does not require a separate iterative phase for each epoch of the learning procedure. In fact, the computational structure is based on the search for saddle points of the Lagrangian in the adjoint space composed of weights, neural outputs (node states), and Lagrange multipliers. The proposed approach is compared experimentally with other popular models for processing graphs.

Neural network quantization methods often involve simulating the quantization process during training. This makes the trained model highly dependent on the precise way quantization is performed. Since low-precision accelerators differ in their quantization policies and their supported mix of data-types, a model trained for one accelerator may not be suitable for another. To address this issue, we propose KURE, a method that provides intrinsic robustness to the model against a broad range of quantization implementations. We show that KURE yields a generic model that may be deployed on numerous inference accelerators without a significant loss in accuracy.

An important problem in multiview representation learning is finding the optimal combination of views with respect to the specific task at hand. To this end, we introduce NAM: a Neural Attentive Multiview machine that learns multiview item representations and similarity by employing a novel attention mechanism. NAM harnesses multiple information sources and automatically quantifies their relevancy with respect to a supervised task. Finally, a very practical advantage of NAM is its robustness to the case of dataset with missing views. We demonstrate the effectiveness of NAM for the task of movies and app recommendations. Our evaluations indicate that NAM outperforms single view models as well as alternative multiview methods on item recommendations tasks, including cold-start scenarios.

Applying machine learning technologies, especially deep learning, into medical image segmentation is being widely studied because of its state-of-the-art performance and results. It can be a key step to provide a reliable basis for clinical diagnosis, such as 3D reconstruction of human tissues, image-guided interventions, image analyzing and visualization. In this review article, deep-learning-based methods for ultrasound image segmentation are categorized into six main groups according to their architectures and training at first. Secondly, for each group, several current representative algorithms are selected, introduced, analyzed and summarized in detail. In addition, common evaluation methods for image segmentation and ultrasound image segmentation datasets are summarized. Further, the performance of the current methods and their evaluations are reviewed. In the end, the challenges and potential research directions for medical ultrasound image segmentation are discussed.

Automating molecular design using deep reinforcement learning (RL) holds the promise of accelerating the discovery of new chemical compounds. A limitation of existing approaches is that they work with molecular graphs and thus ignore the location of atoms in space, which restricts them to 1) generating single organic molecules and 2) heuristic reward functions. To address this, we present a novel RL formulation for molecular design in Cartesian coordinates, thereby extending the class of molecules that can be built. Our reward function is directly based on fundamental physical properties such as the energy, which we approximate via fast quantum-chemical methods. To enable progress towards de-novo molecular design, we introduce MolGym, an RL environment comprising several challenging molecular design tasks along with baselines. In our experiments, we show that our agent can efficiently learn to solve these tasks from scratch by working in a translation and rotation invariant state-action space.

In this paper we study a constraint-based representation of neural network architectures. We cast the learning problem in the Lagrangian framework and we investigate a simple optimization procedure that is well suited to fulfil the so-called architectural constraints, learning from the available supervisions. The computational structure of the proposed Local Propagation (LP) algorithm is based on the search for saddle points in the adjoint space composed of weights, neural outputs, and Lagrange multipliers. All the updates of the model variables are locally performed, so that LP is fully parallelizable over the neural units, circumventing the classic problem of gradient vanishing in deep networks. The implementation of popular neural models is described in the context of LP, together with those conditions that trace a natural connection with Backpropagation. We also investigate the setting in which we tolerate bounded violations of the architectural constraints, and we provide experimental evidence that LP is a feasible approach to train shallow and deep networks, opening the road to further investigations on more complex architectures, easily describable by constraints.

We develop a generic data-driven method for estimator selection in off-policy policy evaluation settings. We establish a strong performance guarantee for the method, showing that it is competitive with the oracle estimator, up to a constant factor. Via in-depth case studies in contextual bandits and reinforcement learning, we demonstrate the generality and applicability of the method. We also perform comprehensive experiments, demonstrating the empirical efficacy of our approach and comparing with related approaches. In both case studies, our method compares favorably with existing methods.

We turn the definition of individual fairness on its head---rather than ascertaining the fairness of a model given a predetermined metric, we find a metric for a given model that satisfies individual fairness. This can facilitate the discussion on the fairness of a model, addressing the issue that it may be difficult to specify a priori a suitable metric. Our contributions are twofold: First, we introduce the definition of a minimal metric and characterize the behavior of models in terms of minimal metrics. Second, for more complicated models, we apply the mechanism of randomized smoothing from adversarial robustness to make them individually fair under a given weighted $L^p$ metric. Our experiments show that adapting the minimal metrics of linear models to more complicated neural networks can lead to meaningful and interpretable fairness guarantees at little cost to utility.

We propose a hierarchical correlation clustering method that extends the well-known correlation clustering to produce hierarchical clusters. We then investigate embedding the respective hierarchy to be used for (tree preserving) embedding and feature extraction. We study the connection of such an embedding to single linkage embedding and minimax distances, and in particular study minimax distances for correlation clustering. Finally, we demonstrate the performance of our methods on several UCI and 20 newsgroup datasets.

In this paper, we study various asymptotic properties (bias, variance, mean squared error, mean integrated squared error, asymptotic normality, uniform strong consistency) for Bernstein estimators of cumulative distribution functions and density functions on the $d$-dimensional simplex. Our results generalize the ones in Leblanc (2012) and Babu et al. (2002), which treated the case $d = 1$, and significantly extend those found in Tenbusch (1994) for the density estimators when $d = 2$. The density estimator (or smoothed histogram) is closely related to the Dirichlet kernel estimator from Ouimet (2020), and can also be used to analyze compositional data.

Separating high-dimensional data like images into independent latent factors remains an open research problem. Here we develop a method that jointly learns a linear independent component analysis (ICA) model with non-linear bijective feature maps. By combining these two methods, ICA can learn interpretable latent structure for images. For non-square ICA, where we assume the number of sources is less than the dimensionality of data, we achieve better unsupervised latent factor discovery than flow-based models and linear ICA. This performance scales to large image datasets such as CelebA

Neural networks and tree ensembles are state-of-the-art learners, each with its unique statistical and computational advantages. We aim to combine these advantages by introducing a new layer for neural networks, composed of an ensemble of differentiable decision trees (a.k.a. soft trees). While differentiable trees demonstrate promising results in the literature, in practice they are typically slow in training and inference as they do not support conditional computation. We mitigate this issue by introducing a new sparse activation function for sample routing, and implement true conditional computation by developing specialized forward and backward propagation algorithms that exploit sparsity. Our efficient algorithms pave the way for jointly training over deep and wide tree ensembles using first-order methods (e.g., SGD). Experiments on 23 classification datasets indicate over 10x speed-ups compared to the differentiable trees used in the literature and over 20x reduction in the number of parameters compared to gradient boosted trees, while maintaining competitive performance. Moreover, experiments on CIFAR, MNIST, and Fashion MNIST indicate that replacing dense layers in CNNs with our tree layer reduces the test loss by 7-53% and the number of parameters by 8x. We provide an open-source TensorFlow implementation with a Keras API.

We provide a novel methodology for computing the most likely path taken by drifters between arbitrary fixed locations in the ocean. We also provide an estimate of the travel time associated with this path. Lagrangian pathways and travel times are of practical value not just in understanding surface velocities, but also in modelling the transport of ocean-borne species such as planktonic organisms, and floating debris such as plastics. In particular, the estimated travel time can be used to compute an estimated Lagrangian distance, which is often more informative than Euclidean distance in understanding connectivity between locations. Our methodology is purely data-driven, and requires no simulations of drifter trajectories, in contrast to existing approaches. Our method scales globally and can simultaneously handle multiple locations in the ocean. Furthermore, we provide estimates of the error and uncertainty associated with both the most likely path and the associated travel time.

Outlier, or anomaly, detection is essential for optimal performance of machine learning methods and statistical predictive models. It is not just a technical step in a data cleaning process but a key topic in many fields such as fraudulent document detection, in medical applications and assisted diagnosis systems or detecting security threats. In contrast to population-based methods, neighborhood based local approaches are simple flexible methods that have the potential to perform well in small sample size unbalanced problems. However, a main concern of local approaches is the impact that the computation of each sample neighborhood has on the method performance. Most approaches use a distance in the feature space to define a single neighborhood that requires careful selection of several parameters. This work presents a local approach based on a local measure of the heterogeneity of sample labels in the feature space considered as a topological manifold. Topology is computed using the communities of a weighted graph codifying mutual nearest neighbors in the feature space. This way, we provide with a set of multiple neighborhoods able to describe the structure of complex spaces without parameter fine tuning. The extensive experiments on real-world data sets show that our approach overall outperforms, both, local and global strategies in multi and single view settings.

Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However this sparsity tends not to be homogeneous, and networks can also be locally dense, for example with a few nodes connecting to a large fraction of the rest of the network, or with small groups of nodes with a large probability of connections between them. Here we show how latent Poisson models which generate hidden multigraphs can be effective at capturing this density heterogeneity, while being more tractable mathematically than some of the alternatives that model simple graphs directly. We show how these latent multigraphs can be reconstructed from data on simple graphs, and how this allows us to disentangle dissortative degree-degree correlations from the constraints of imposed degree sequences, and to improve the identification of community structure in empirically relevant scenarios.

The design of symbol detectors in digital communication systems has traditionally relied on statistical channel models that describe the relation between the transmitted symbols and the observed signal at the receiver. Here we review a data-driven framework to symbol detection design which combines machine learning (ML) and model-based algorithms. In this hybrid approach, well-known channel-model-based algorithms such as the Viterbi method, BCJR detection, and multiple-input multiple-output (MIMO) soft interference cancellation (SIC) are augmented with ML-based algorithms to remove their channel-model-dependence, allowing the receiver to learn to implement these algorithms solely from data. The resulting data-driven receivers are most suitable for systems where the underlying channel models are poorly understood, highly complex, or do not well-capture the underlying physics. Our approach is unique in that it only replaces the channel-model-based computations with dedicated neural networks that can be trained from a small amount of data, while keeping the general algorithm intact. Our results demonstrate that these techniques can yield near-optimal performance of model-based algorithms without knowing the exact channel input-output statistical relationship and in the presence of channel state information uncertainty.

On 12 February 2020 the Royal Statistical Society hosted a meeting to discuss the forthcoming paper Graphical models for extremes'' by Sebastian Engelke and Adrien Hitz [arXiv:1812.01734]. This short note is a supplement to my discussion contribution. It contains the proofs. It is shown that the traditional notion of extremal independence agrees with the newly introduced notion of extremal independence, which subsequently allows for a meaningful interpretation of disconnected graphs in the context of the discussion paper. The notation and references used in this note are adopted from the discussion paper.

In 2007, and in a series of later papers, Joy Christian claimed to refute Bell's theorem, presenting an alleged local realistic model of the singlet correlations using techniques from Geometric Algebra (GA). Several authors published papers refuting his claims, and Christian's ideas did not gain acceptance. However, he recently succeeded in publishing yet more ambitious and complex versions of his theory in fairly mainstream journals. How could this be? The mathematics and logic of Bell's theorem is simple and transparent and has been intensely studied and debated for over 50 years. Christian claims to have a mathematical counterexample to a purely mathematical theorem. Each new version of Christian's model used new devices to circumvent Bell's theorem or depended on a new way to misunderstand Bell's work. These devices and misinterpretations are in common use by other Bell critics, so it useful to identify and name them. I hope that this paper can serve as a useful resource to those who need to evaluate new "disproofs of Bell's theorem". Christian's fundamental idea is simple and quite original: he gives a probabilistic interpretation of the fundamental GA equation a.b = (ab + ba)/2. After that, ambiguous notation and technical complexity allow sign errors to be hidden from sight, and new mathematical errors can be introduced. This version: as published, but with correction note added.

The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind consists of striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind consists of a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note, I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained "for free": they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a "spinning coloured disk" model, and a research programme: describe these functions in a concise analytic way. We survey open problems, and we show that the widespread idea that "quantum correlations are more extreme than classical physics allows" is at best highly inaccurate, through giving a concrete example of a classical correlation which satisfies all the symmetries and all the certainty relations and which exceeds the quantum correlations over a whole range of settings

There is a renewed interest in polynomial regression in the form of identifying influential interactions between features. In many settings, this takes place in a high-dimensional model, making the number of interactions unwieldy or computationally infeasible. Furthermore, it is difficult to analyze such spaces directly as they are often highly correlated. Standard feature selection issues remain such as how to determine a final model which generalizes well. This paper solves these problems with a sequential algorithm called Revisiting Alpha-Investing (RAI). RAI is motivated by the principle of marginality and searches the feature-space of higher-order interactions by greedily building upon lower-order terms. RAI controls a notion of false rejections and comes with a performance guarantee relative to the best-subset model. This ensures that signal is identified while providing a valid stopping criterion to prevent over-selection. We apply RAI in a novel setting over a family of regressions in order to select gene-specific interaction models for differential expression profiling.

We present a novel inference approach that we call Sample Out-of-Sample (or SOS) inference. The approach can be used widely, ranging from semi-supervised learning to stress testing, and it is fundamental in the application of data-driven Distributionally Robust Optimization (DRO). Our method enables measuring the impact of plausible out-of-sample scenarios in a given performance measure of interest, such as a financial loss. The methodology is inspired by Empirical Likelihood (EL), but we optimize the empirical Wasserstein distance (instead of the empirical likelihood) induced by observations. From a methodological standpoint, our analysis of the asymptotic behavior of the induced Wasserstein-distance profile function shows dramatic qualitative differences relative to EL. For instance, in contrast to EL, which typically yields chi-squared weak convergence limits, our asymptotic distributions are often not chi-squared. Also, the rates of convergence that we obtain have some dependence on the dimension in a non-trivial way but remain controlled as the dimension increases.

This paper studies models in which hypothesis tests have trivial power, that is, power smaller than size. This testing impossibility, or impossibility type A, arises when any alternative is not distinguishable from the null. We also study settings in which it is impossible to have almost surely bounded confidence sets for a parameter of interest. This second type of impossibility (type B) occurs under a condition weaker than the condition for type A impossibility: the parameter of interest must be nearly unidentified. Our theoretical framework connects many existing publications on impossible inference that rely on different notions of topologies to show models are not distinguishable or nearly unidentified. We also derive both types of impossibility using the weak topology induced by convergence in distribution. Impossibility in the weak topology is often easier to prove, it is applicable for many widely-used tests, and it is useful for robust hypothesis testing. We conclude by demonstrating impossible inference in multiple economic applications of models with discontinuity and time-series models.

This article proposes different tests for treatment effect heterogeneity when the outcome of interest, typically a duration variable, may be right-censored. The proposed tests study whether a policy 1) has zero distributional (average) effect for all subpopulations defined by covariate values, and 2) has homogeneous average effect across different subpopulations. The proposed tests are based on two-step Kaplan-Meier integrals and do not rely on parametric distributional assumptions, shape restrictions, or on restricting the potential treatment effect heterogeneity across different subpopulations. Our framework is suitable not only to exogenous treatment allocation but can also account for treatment noncompliance - an important feature in many applications. The proposed tests are consistent against fixed alternatives, and can detect nonparametric alternatives converging to the null at the parametric $n^{-1/2}$-rate, $n$ being the sample size. Critical values are computed with the assistance of a multiplier bootstrap. The finite sample properties of the proposed tests are examined by means of a Monte Carlo study and an application about the effect of labor market programs on unemployment duration. Open-source software is available for implementing all proposed tests.

We describe semiparametric estimation and inference for causal effects using observational data from a single social network. Our asymptotic result is the first to allow for dependence of each observation on a growing number of other units as sample size increases. While previous methods have generally implicitly focused on one of two possible sources of dependence among social network observations, we allow for both dependence due to transmission of information across network ties, and for dependence due to latent similarities among nodes sharing ties. We describe estimation and inference for new causal effects that are specifically of interest in social network settings, such as interventions on network ties and network structure. Using our methods to reanalyze the Framingham Heart Study data used in one of the most influential and controversial causal analyses of social network data, we find that after accounting for network structure there is no evidence for the causal effects claimed in the original paper.

In this paper we introduce the Kumaraswamy autoregressive moving average models (KARMA), which is a dynamic class of models for time series taking values in the double bounded interval $(a,b)$ following the Kumaraswamy distribution. The Kumaraswamy family of distribution is widely applied in many areas, especially hydrology and related fields. Classical examples are time series representing rates and proportions observed over time. In the proposed KARMA model, the median is modeled by a dynamic structure containing autoregressive and moving average terms, time-varying regressors, unknown parameters and a link function. We introduce the new class of models and discuss conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis and forecasting. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. An application to environmental real data is presented and discussed.

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e. misspecified) mixture models. These identifiability conditions generalize existing conditions in the literature, and are flexible enough to include for example mixtures of Gaussian mixtures. In contrast to the recent literature on estimating nonparametric mixtures, we allow for general nonparametric mixture components, and instead impose regularity assumptions on the underlying mixing measure. As our primary application, we apply these results to partition-based clustering, generalizing the notion of a Bayes optimal partition from classical parametric model-based clustering to nonparametric settings. Furthermore, this framework is constructive so that it yields a practical algorithm for learning identified mixtures, which is illustrated through several examples on real data. The key conceptual device in the analysis is the convex, metric geometry of probability measures on metric spaces and its connection to the Wasserstein convergence of mixing measures. The result is a flexible framework for nonparametric clustering with formal consistency guarantees.

Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using subsampling methods from randomized numerical linear algebra. We derive a simulation technique whose runtime scales polynomially in the number of qubits and the Frobenius norm of the Hamiltonian. As an immediate application, we show that sample based quantum simulation, a type of evolution where the Hamiltonian is a density matrix, can be efficiently classically simulated under specific structural conditions. Our main technical contribution is a randomized algorithm for approximating Hermitian matrix exponentials. The proof leverages a low-rank, symmetric approximation via the Nystr\"om method. Our results suggest that under strong sampling assumptions there exist classical poly-logarithmic time simulations of quantum computations.

A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by embedding regularized estimators for the state-dependent covariance matrices and autoregression matrices in the M-step. The performance of the proposed regularized estimators is evaluated both in the simulation experiments and on the New York Stock Exchange financial portfolio data.

A reparametrized Dirichlet-multinomial distribution is introduced, and the covariance matrix, as well as, the algorithm for calculating the PDF for n species are provided. The distribution is suited for modelling the joint distribution of pin-point cover data of spatially aggregated plant species, and the parametrization ensures that the degree of spatially aggregation is modelled by a parameter and the mean cover of the species is modelled by the other parameters. This last property is convenient for using the distribution in Bayesian hierarchical models where the mean cover of the different species typically is modelled as latent variables.

Learning algorithms are enabling robots to solve increasingly challenging real-world tasks. These approaches often rely on demonstrations and reproduce the behavior shown. Unexpected changes in the environment may require using different behaviors to achieve the same effect, for instance to reach and grasp an object in changing clutter. An emerging paradigm addressing this robustness issue is to learn a diverse set of successful behaviors for a given task, from which a robot can select the most suitable policy when faced with a new environment. In this paper, we explore a novel realization of this vision by learning a generative model over policies. Rather than learning a single policy, or a small fixed repertoire, our generative model for policies compactly encodes an unbounded number of policies and allows novel controller variants to be sampled. Leveraging our generative policy network, a robot can sample novel behaviors until it finds one that works for a new environment. We demonstrate this idea with an application of robust ball-throwing in the presence of obstacles. We show that this approach achieves a greater diversity of behaviors than an existing evolutionary approach, while maintaining good efficacy of sampled behaviors, allowing a Baxter robot to hit targets more often when ball throwing in the presence of obstacles.

Phase I dose-escalation trials constitute the first step in investigating the safety of potentially promising drugs in humans. Conventional methods for phase I dose-escalation trials are based on a single treatment schedule only. In medical practice, however, multiple schedules are more frequently investigated in the same trial. Investigation of the acceptable dose and schedule combination in a phase I trial can be done simultaneously or sequentially. Here, we consider the latter, sequential phase I trials, where the trial proceeds with a new schedule (e.g. daily or weekly dosing) once the dose escalation with another schedule has been completed. The aim is to utilize the information from both the completed and the ongoing dose-escalation trial to inform decisions on the dose level for the next dose cohort. For this purpose, we propose to use the time-to-event pharmacokinetics (TITE-PK) model which can integrate information from multiple schedules using pharmacokinetics (PK) principles. In a simulation study, we used the Bayesian Logistic Regression Model (BLRM) as the comparator, which only considers the number of DLT occurred, not the time-to-first DLT, and uses an ad-hoc approach to analyze multiple schedules. TITE-PK results in better performance compared to the BLRM in terms of recommending acceptable dose for sequential phase I trials in most of the scenarios considered. The \texttt{R} and \texttt{Stan} code for the implementation of an illustrative sequential phase I trial example is publicly available (\url{https://github.com/gunhanb/TITEPK_sequential}).

In this paper we study the problem of testing if an $L_2-$function $f$ belonging to a certain $l_2$-Sobolev-ball $B_t(R)$ of radius $R>0$ with smoothness level $t>0$ indeed exhibits a higher smoothness level $s>t$, that is, belongs to $B_s(R)$. We assume that only a perturbed version of $f$ is available, where the noise is governed by a standard Brownian motion scaled by $\frac{1}{\sqrt{n}}$. More precisely, considering a testing problem of the form $$H_0:~f\in B_s(R)~~\mathrm{vs.}~~H_1:~f\in B_t(R),~\inf_{h\in B_s}\Vert f-h\Vert_{L_2}>\rho$$ for some $\rho>0$, we approach the task of identifying the smallest value for $\rho$, denoted $\rho^\ast$, enabling the existence of a test $\varphi$ with small error probability in a minimax sense. By deriving lower and upper bounds on $\rho^\ast$, we expose its precise dependence on $n$: $$\rho^\ast\sim n^{-\frac{t}{2t+1/2}}.$$ As a remarkable aspect of this composite-composite testing problem, it turns out that the rate does not depend on $s$ and is equal to the rate in signal-detection, i.e. the case of a simple null hypothesis.

Metric-based meta-learning techniques have successfully been applied to few-shot classification problems. In this paper, we propose to leverage cross-modal information to enhance metric-based few-shot learning methods. Visual and semantic feature spaces have different structures by definition. For certain concepts, visual features might be richer and more discriminative than text ones. While for others, the inverse might be true. Moreover, when the support from visual information is limited in image classification, semantic representations (learned from unsupervised text corpora) can provide strong prior knowledge and context to help learning. Based on these two intuitions, we propose a mechanism that can adaptively combine information from both modalities according to new image categories to be learned. Through a series of experiments, we show that by this adaptive combination of the two modalities, our model outperforms current uni-modality few-shot learning methods and modality-alignment methods by a large margin on all benchmarks and few-shot scenarios tested. Experiments also show that our model can effectively adjust its focus on the two modalities. The improvement in performance is particularly large when the number of shots is very small.

We introduce data-driven decision-making algorithms that achieve state-of-the-art \emph{dynamic regret} bounds for non-stationary bandit settings. These settings capture applications such as advertisement allocation, dynamic pricing, and traffic network routing in changing environments. We show how the difficulty posed by the (unknown \emph{a priori} and possibly adversarial) non-stationarity can be overcome by an unconventional marriage between stochastic and adversarial bandit learning algorithms. Our main contribution is a general algorithmic recipe for a wide variety of non-stationary bandit problems. Specifically, we design and analyze the sliding window-upper confidence bound algorithm that achieves the optimal dynamic regret bound for each of the settings when we know the respective underlying \emph{variation budget}, which quantifies the total amount of temporal variation of the latent environments. Boosted by the novel bandit-over-bandit framework that adapts to the latent changes, we can further enjoy the (nearly) optimal dynamic regret bounds in a (surprisingly) parameter-free manner. In addition to the classical exploration-exploitation trade-off, our algorithms leverage the power of the forgetting principle" in the learning processes, which is vital in changing environments. Our extensive numerical experiments on both synthetic and real world online auto-loan datasets show that our proposed algorithms achieve superior empirical performance compared to existing algorithms.

Human annotations serve an important role in computational models where the target constructs under study are hidden, such as dimensions of affect. This is especially relevant in machine learning, where subjective labels derived from related observable signals (e.g., audio, video, text) are needed to support model training and testing. Current research trends focus on correcting artifacts and biases introduced by annotators during the annotation process while fusing them into a single annotation. In this work, we propose a novel annotation approach using triplet embeddings. By lifting the absolute annotation process to relative annotations where the annotator compares individual target constructs in triplets, we leverage the accuracy of comparisons over absolute ratings by human annotators. We then build a 1-dimensional embedding in Euclidean space that is indexed in time and serves as a label for regression. In this setting, the annotation fusion occurs naturally as a union of sets of sampled triplet comparisons among different annotators. We show that by using our proposed sampling method to find an embedding, we are able to accurately represent synthetic hidden constructs in time under noisy sampling conditions. We further validate this approach using human annotations collected from Mechanical Turk and show that we can recover the underlying structure of the hidden construct up to bias and scaling factors.

We first pose the Unsupervised Progressive Learning (UPL) problem: learning salient representations from a non-stationary stream of unlabeled data in which the number of object classes increases with time. To solve the UPL problem we propose an architecture that involves a module called Self-Taught Associative Memory (STAM). Layered hierarchies of STAM modules learn based on a combination of online clustering, novelty detection, forgetting outliers, and storing only prototypical representations rather than specific examples. We evaluate STAM representations using clustering and classification tasks, relying on limited labeled data for the latter. Even though there are no prior approaches that are directly applicable to the UPL problem, we compare the STAM architecture to a couple of unsupervised and self-supervised deep learning approaches adapted in the UPL context.

Predicting scalar outcomes using functional predictors is a classic problem in functional data analysis. In many applications, however, only specific locations or time-points of the functional predictors have an impact on the outcome. Such points of impact'' are typically unknown and have to be estimated in addition to estimating the usual model components. We show that our points of impact estimator enjoys a super-consistent convergence rate and does not require knowledge or pre-estimates of the unknown model components. This remarkable result facilitates the subsequent estimation of the remaining model components as shown in the theoretical part, where we consider the case of nonparametric models and the practically relevant case of generalized linear models. The finite sample properties of our estimators are assessed by means of a simulation study. Our methodology is motivated by data from a psychological experiment in which the participants were asked to continuously rate their emotional state while watching an affective video eliciting a varying intensity of emotional reactions.

A/B testing is of central importance in the industry, especially in the technology sector where companies run long sequences of A/B tests to optimize their products. Since the space of potential innovations is typically vast, the experimenter must make quick and good decisions without wasting too much time on a single A/B test in the sequence. In particular, discarding an innovation with a small benefit might be better in the long run than using many samples to precisely determine its value. In this work, we introduce a performance measure that captures this idea and design an efficient algorithm that performs almost as well as the best A/B strategy in a given set. As it turns out, a key technical difficulty that significantly affects the learning rates is the hardness of obtaining unbiased estimates of the strategy rewards.

We introduce a probabilistic approach to unify deep continual learning with open set recognition, based on variational Bayesian inference. Our single model combines a joint probabilistic encoder with a generative model and a linear classifier that get shared across sequentially arriving tasks. In order to successfully distinguish unseen unknown data from trained known tasks, we propose to bound the class specific approximate posterior by fitting regions of high density on the basis of correctly classified data points. These bounds are further used to significantly alleviate catastrophic forgetting by avoiding samples from low density areas in generative replay. Our approach requires no storing of old- or upfront knowledge of future data and is empirically validated on visual and audio tasks in class incremental, as well as cross-dataset scenarios across modalities.

Explaining decisions of deep neural networks is a hot research topic with applications in medical imaging, video surveillance, and self driving cars. Many methods have been proposed in literature to explain these decisions by identifying relevance of different pixels, limiting the types of explanations possible. In this paper, we propose a method that can generate contrastive explanations for such data where we not only highlight aspects that are in themselves sufficient to justify the classification by the deep model, but also new aspects which if added will change the classification. In order to move beyond the limitations of previous explanations, our key contribution is how we define "addition" for such rich data in a formal yet humanly interpretable way that leads to meaningful results. This was one of the open questions laid out in in Dhurandhar et.al. (2018) [6], which proposed a general framework for creating (local) contrastive explanations for deep models, but is limited to simple use cases such as black/white images. We showcase the efficacy of our approach on three diverse image data sets (faces, skin lesions, and fashion apparel) in creating intuitive explanations that are also quantitatively superior compared with other state-of-the-art interpretability methods. A thorough user study with 200 individuals asks how well the various methods are understood by humans and demonstrates which aspects of contrastive explanations are most desirable.

Recent work by Jacot et al. (2018) has showed that training a neural network of any kind with gradient descent in parameter space is equivalent to kernel gradient descent in function space with Recent influential work by Jacot et al. (2018) has shown that training a neural network of any kind with gradient descent in parameter space is strongly related to kernel gradient descent in function space with respect to the Neural Tangent Kernel (NTK). Lee et al. (2019) built on this result by establishing that the output of a neural network trained using gradient descent can be approximated by a linear model for wide networks. In parallel, a recent line of studies (Schoenholz et al. (2017), Hayou et al. (2019)) has suggested that a special initialization known as the Edge of Chaos improves training. In this paper, we bridge the gap between these two concepts by quantifying the impact of the initialization and the activation function on the NTK when the network depth becomes large. We provide experiments illustrating our theoretical results.

We study gradient compression methods to alleviate the communication bottleneck in data-parallel distributed optimization. Despite the significant attention received, current compression schemes either do not scale well or fail to achieve the target test accuracy. We propose a new low-rank gradient compressor based on power iteration that can i) compress gradients rapidly, ii) efficiently aggregate the compressed gradients using all-reduce, and iii) achieve test performance on par with SGD. The proposed algorithm is the only method evaluated that achieves consistent wall-clock speedups when benchmarked against regular SGD with an optimized communication backend. We demonstrate reduced training times for convolutional networks as well as LSTMs on common datasets. Our code is available at https://github.com/epfml/powersgd.

We propose a novel score-based approach to learning a directed acyclic graph (DAG) from observational data. We adapt a recently proposed continuous constrained optimization formulation to allow for nonlinear relationships between variables using neural networks. This extension allows to model complex interactions while avoiding the combinatorial nature of the problem. In addition to comparing our method to existing continuous optimization methods, we provide missing empirical comparisons to nonlinear greedy search methods. On both synthetic and real-world data sets, this new method outperforms current continuous methods on most tasks, while being competitive with existing greedy search methods on important metrics for causal inference.

We improve the over-parametrization size over two beautiful results [Li and Liang' 2018] and [Du, Zhai, Poczos and Singh' 2019] in deep learning theory.

We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension $n$ is large relative to the sample size $T$). In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided $\log^{3}n/(n^{2-\beta_1}T)\rightarrow0$ and $\log^2n/T\to 0$, where $\beta_1$ is some measure of cross-sectional dependence. We obtain the limiting distributions of Lagrange multiplier (LM) and Wald tests under both the null and local alternatives concerning the mean vector $\mu$. Testing linear restrictions of $\mu$ is also investigated. Finally, our methodology performs well in the finite-sample situations both when the Kronecker product model is true, and when it is not true.

Inverse problem is ubiquitous in science and engineering, and Bayesian methodologies are often used to infer the underlying parameters. For high dimensional temporal-spatial models, classical Markov chain Monte Carlo (MCMC) methods are often slow to converge, and it is necessary to apply Metropolis-within-Gibbs (MwG) sampling on parameter blocks. However, the computation cost of each MwG iteration is typically $O(n^2)$, where $n$ is the model dimension. This can be too expensive in practice. This paper introduces a new reduced computation method to bring down the computation cost to $O(n)$, for the inverse initial value problem of a stochastic differential equation (SDE) with local interactions. The key observation is that each MwG proposal is only different from the original iterate at one parameter block, and this difference will only propagate within a local domain in the SDE computations. Therefore we can approximate the global SDE computation with a surrogate updated only within the local domain for reduced computation cost. Both theoretically and numerically, we show that the approximation errors can be controlled by the local domain size. We discuss how to implement the local computation scheme using Euler--Maruyama and 4th order Runge--Kutta methods. We numerically demonstrate the performance of the proposed method with the Lorenz 96 model and a linear stochastic flow model.

Learning to disentangle the hidden factors of variations within a set of observations is a key task for artificial intelligence. We present a unified formulation for class and content disentanglement and use it to illustrate the limitations of current methods. We therefore introduce LORD, a novel method based on Latent Optimization for Representation Disentanglement. We find that latent optimization, along with an asymmetric noise regularization, is superior to amortized inference for achieving disentangled representations. In extensive experiments, our method is shown to achieve better disentanglement performance than both adversarial and non-adversarial methods that use the same level of supervision. We further introduce a clustering-based approach for extending our method for settings that exhibit in-class variation with promising results on the task of domain translation.

Data selection methods, such as active learning and core-set selection, are useful tools for machine learning on large datasets. However, they can be prohibitively expensive to apply in deep learning because they depend on feature representations that need to be learned. In this work, we show that we can greatly improve the computational efficiency by using a small proxy model to perform data selection (e.g., selecting data points to label for active learning). By removing hidden layers from the target model, using smaller architectures, and training for fewer epochs, we create proxies that are an order of magnitude faster to train. Although these small proxy models have higher error rates, we find that they empirically provide useful signals for data selection. We evaluate this "selection via proxy" (SVP) approach on several data selection tasks across five datasets: CIFAR10, CIFAR100, ImageNet, Amazon Review Polarity, and Amazon Review Full. For active learning, applying SVP can give an order of magnitude improvement in data selection runtime (i.e., the time it takes to repeatedly train and select points) without significantly increasing the final error (often within 0.1%). For core-set selection on CIFAR10, proxies that are over 10x faster to train than their larger, more accurate targets can remove up to 50% of the data without harming the final accuracy of the target, leading to a 1.6x end-to-end training time improvement.

We propose a fast, model agnostic method for finding interpretable counterfactual explanations of classifier predictions by using class prototypes. We show that class prototypes, obtained using either an encoder or through class specific k-d trees, significantly speed up the the search for counterfactual instances and result in more interpretable explanations. We introduce two novel metrics to quantitatively evaluate local interpretability at the instance level. We use these metrics to illustrate the effectiveness of our method on an image and tabular dataset, respectively MNIST and Breast Cancer Wisconsin (Diagnostic). The method also eliminates the computational bottleneck that arises because of numerical gradient evaluation for $\textit{black box}$ models.

Adversarial examples raise questions about whether neural network models are sensitive to the same visual features as humans. In this paper, we first detect adversarial examples or otherwise corrupted images based on a class-conditional reconstruction of the input. To specifically attack our detection mechanism, we propose the Reconstructive Attack which seeks both to cause a misclassification and a low reconstruction error. This reconstructive attack produces undetected adversarial examples but with much smaller success rate. Among all these attacks, we find that CapsNets always perform better than convolutional networks. Then, we diagnose the adversarial examples for CapsNets and find that the success of the reconstructive attack is highly related to the visual similarity between the source and target class. Additionally, the resulting perturbations can cause the input image to appear visually more like the target class and hence become non-adversarial. This suggests that CapsNets use features that are more aligned with human perception and have the potential to address the central issue raised by adversarial examples.

We study the algorithmic problem of estimating the mean of heavy-tailed random vector in $\mathbb{R}^d$, given $n$ i.i.d. samples. The goal is to design an efficient estimator that attains the optimal sub-gaussian error bound, only assuming that the random vector has bounded mean and covariance. Polynomial-time solutions to this problem are known but have high runtime due to their use of semi-definite programming (SDP). Conceptually, it remains open whether convex relaxation is truly necessary for this problem.

In this work, we show that it is possible to go beyond SDP and achieve better computational efficiency. In particular, we provide a spectral algorithm that achieves the optimal statistical performance and runs in time $\widetilde O\left(n^2 d \right)$, improving upon the previous fastest runtime $\widetilde O\left(n^{3.5}+ n^2d\right)$ by Cherapanamjeri el al. (COLT '19). Our algorithm is spectral in that it only requires (approximate) eigenvector computations, which can be implemented very efficiently by, for example, power iteration or the Lanczos method.

At the core of our algorithm is a novel connection between the furthest hyperplane problem introduced by Karnin et al. (COLT '12) and a structural lemma on heavy-tailed distributions by Lugosi and Mendelson (Ann. Stat. '19). This allows us to iteratively reduce the estimation error at a geometric rate using only the information derived from the top singular vector of the data matrix, leading to a significantly faster running time.

When an agent acquires new information, ideally it would immediately be capable of using that information to understand its environment. This is not possible using conventional deep neural networks, which suffer from catastrophic forgetting when they are incrementally updated, with new knowledge overwriting established representations. A variety of approaches have been developed that attempt to mitigate catastrophic forgetting in the incremental batch learning scenario, where a model learns from a series of large collections of labeled samples. However, in this setting, inference is only possible after a batch has been accumulated, which prohibits many applications. An alternative paradigm is online learning in a single pass through the training dataset on a resource constrained budget, which is known as streaming learning. Streaming learning has been much less studied in the deep learning community. In streaming learning, an agent learns instances one-by-one and can be tested at any time, rather than only after learning a large batch. Here, we revisit streaming linear discriminant analysis, which has been widely used in the data mining research community. By combining streaming linear discriminant analysis with deep learning, we are able to outperform both incremental batch learning and streaming learning algorithms on both ImageNet ILSVRC-2012 and CORe50, a dataset that involves learning to classify from temporally ordered samples.

Machine-learning (ML) algorithms or models, especially deep neural networks (DNNs), have shown significant promise in several areas. However, researchers have recently demonstrated that ML algorithms, especially DNNs, are vulnerable to adversarial examples (slightly perturbed samples that cause misclassification). The existence of adversarial examples has hindered the deployment of ML algorithms in safety-critical sectors, such as security. Several defenses for adversarial examples exist in the literature. One of the important classes of defenses are manifold-based defenses, where a sample is pulled back" into the data manifold before classifying. These defenses rely on the assumption that data lie in a manifold of a lower dimension than the input space. These defenses use a generative model to approximate the input distribution. In this paper, we investigate the following question: do the generative models used in manifold-based defenses need to be topology-aware? We suggest the answer is yes, and we provide theoretical and empirical evidence to support our claim.

As the use of black-box models becomes ubiquitous in high stake decision-making systems, demands for fair and interpretable models are increasing. While it has been shown that interpretable models can be as accurate as black-box models in several critical domains, existing fair classification techniques that are interpretable by design often display poor accuracy/fairness tradeoffs in comparison with their non-interpretable counterparts. In this paper, we propose FairCORELS, a fair classification technique interpretable by design, whose objective is to learn fair rule lists. Our solution is a multi-objective variant of CORELS, a branch-and-bound algorithm to learn rule lists, that supports several statistical notions of fairness. Examples of such measures include statistical parity, equal opportunity and equalized odds. The empirical evaluation of FairCORELS on real-world datasets demonstrates that it outperforms state-of-the-art fair classification techniques that are interpretable by design while being competitive with non-interpretable ones.

Many relevant applications in the environmental and socioeconomic sciences use areal data, such as biodiversity checklists, agricultural statistics, or socioeconomic surveys. For applications that surpass the spatial, temporal or thematic scope of any single data source, data must be integrated from several heterogeneous sources. Inconsistent concepts, definitions, or messy data tables make this a tedious and error-prone process. To date, a dedicated tool for organising areal data is still lacking. Here, we introduce the R package \texttt{arealDB} that integrates heterogeneous areal data and associated geometries into a consistent database. It is useful for harmonising language and semantics of variables, relating data to geometries, and documenting metadata and provenance. We illustrate the functionality by integrating two disparate datasets (Brazil, USA) on the harvested area of soybean. The easy-to-use tools in \texttt{arealDB} promise quality-improvements to downstream scientific, monitoring, and management applications but also substantial time-savings to database collation efforts.

Addressing the non-uniform missing mechanism of rating feedback is critical to build a well-performing recommeder in the real-world systems. To tackle the challenging issue, we first define an ideal loss function that should be optimized to achieve the goal of recommendation. Then, we derive the generalization error bound of the ideal loss that alleviates the variance and the misspecification problems of the previous propensity-based methods. We further propose a meta-learning method minimizing the bound. Empirical evaluation using real-world datasets validates the theoretical findings and demonstrates the practical advantages of the proposed upper bound minimization approach.

Generating visualizations and interpretations from high-dimensional data is a common problem in many applications. Two key approaches for tackling this problem are clustering and representation learning. On the one hand, there are very performant deep clustering models, such as DEC and IDEC. On the other hand, there are interpretable representation learning techniques, often relying on latent topological structures such as self-organizing maps. However, current methods do not yet successfully combine these two approaches. We present a novel way to fit self-organizing maps with probabilistic cluster assignments, PSOM, a new deep architecture for probabilistic clustering, DPSOM, and its extension to time series data, T-DPSOM. We show that they achieve superior clustering performance compared to current deep clustering methods on static MNIST/Fashion-MNIST data as well as medical time series, while also inducing an interpretable representation. Moreover, on medical time series, T-DPSOM successfully predicts future trajectories in the original data space.

Scalability in terms of object density in a scene is a primary challenge in unsupervised sequential object-oriented representation learning. Most of the previous models have been shown to work only on scenes with a few objects. In this paper, we propose SCALOR, a probabilistic generative model for learning SCALable Object-oriented Representation of a video. With the proposed spatially-parallel attention and proposal-rejection mechanisms, SCALOR can deal with orders of magnitude larger numbers of objects compared to the previous state-of-the-art models. Additionally, we introduce a background module that allows SCALOR to model complex dynamic backgrounds as well as many foreground objects in the scene. We demonstrate that SCALOR can deal with crowded scenes containing up to a hundred objects while jointly modeling complex dynamic backgrounds. Importantly, SCALOR is the first unsupervised object representation model shown to work for natural scenes containing several tens of moving objects.

It is important to collect credible training samples $(x,y)$ for building data-intensive learning systems (e.g., a deep learning system). In the literature, there is a line of studies on eliciting distributional information from self-interested agents who hold relevant information. Asking people to report complex distribution $p(x)$, though theoretically viable, is challenging in practice. This is primarily due to the heavy cognitive loads required for human agents to reason and report this high dimensional information. This paper introduces a deep learning aided method to incentivize credible sample contributions from selfish and rational agents. The challenge to do so is to design an incentive-compatible score function to score each reported sample to induce truthful reports, instead of an arbitrary or even adversarial one. We show that with accurate estimation of a certain $f$-divergence function we are able to achieve approximate incentive compatibility in eliciting truthful samples. We then present an efficient estimator with theoretical guarantee via studying the variational forms of $f$-divergence function. Our work complements the literature of information elicitation via introducing \emph{sample elicitation}. We also show a connection between this sample elicitation problem and $f$-GAN, and how this connection can help reconstruct an estimator of the distribution based on collected samples. Thorough numerical experiments are conducted to validate our designed mechanisms.

Deployment and operation of autonomous underwater vehicles is expensive and time-consuming. High-quality realistic sonar data simulation could be of benefit to multiple applications, including training of human operators for post-mission analysis, as well as tuning and validation of autonomous target recognition (ATR) systems for underwater vehicles. Producing realistic synthetic sonar imagery is a challenging problem as the model has to account for specific artefacts of real acoustic sensors, vehicle altitude, and a variety of environmental factors. We propose a novel method for generating realistic-looking sonar side-scans of full-length missions, called Markov Conditional pix2pix (MC-pix2pix). Quantitative assessment results confirm that the quality of the produced data is almost indistinguishable from real. Furthermore, we show that bootstrapping ATR systems with MC-pix2pix data can improve the performance. Synthetic data is generated 18 times faster than real acquisition speed, with full user control over the topography of the generated data.

We introduce an alternative closed form lower bound on the Gaussian process ($\mathcal{GP}$) likelihood based on the R\'enyi $\alpha$-divergence. This new lower bound can be viewed as a convex combination of the Nystr\"om approximation and the exact $\mathcal{GP}$. The key advantage of this bound, is its capability to control and tune the enforced regularization on the model and thus is a generalization of the traditional variational $\mathcal{GP}$ regression. From a theoretical perspective, we provide the convergence rate and risk bound for inference using our proposed approach. Experiments on real data show that the proposed algorithm may be able to deliver improvement over several $\mathcal{GP}$ inference methods.

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called "higher-order interactions" that involve more than two nodes at a time. However, we have fewer rigorous methods that can provide insight from such representations. Here, we develop a computational framework for the problem of clustering hypergraphs with categorical edge labels --- or different interaction types --- where clusters corresponds to groups of nodes that frequently participate in the same type of interaction.

Our methodology is based on a combinatorial objective function that is related to correlation clustering on graphs but enables the design of much more efficient algorithms that also seamlessly generalize to hypergraphs. When there are only two label types, our objective can be optimized in polynomial time, using an algorithm based on minimum cuts. Minimizing our objective becomes NP-hard with more than two label types, but we develop fast approximation algorithms based on linear programming relaxations that have theoretical cluster quality guarantees. We demonstrate the efficacy of our algorithms and the scope of the model through problems in edge-label community detection, clustering with temporal data, and exploratory data analysis.

Consequential decision-making incentivizes individuals to strategically adapt their behavior to the specifics of the decision rule. While a long line of work has viewed strategic adaptation as gaming and attempted to mitigate its effects, recent work has instead sought to design classifiers that incentivize individuals to improve a desired quality. Key to both accounts is a cost function that dictates which adaptations are rational to undertake. In this work, we develop a causal framework for strategic adaptation. Our causal perspective clearly distinguishes between gaming and improvement and reveals an important obstacle to incentive design. We prove any procedure for designing classifiers that incentivize improvement must inevitably solve a non-trivial causal inference problem. Moreover, we show a similar result holds for designing cost functions that satisfy the requirements of previous work. With the benefit of hindsight, our results show much of the prior work on strategic classification is causal modeling in disguise.

The performance of optimizers, particularly in deep learning, depends considerably on their chosen hyperparameter configuration. The efficacy of optimizers is often studied under near-optimal problem-specific hyperparameters, and finding these settings may be prohibitively costly for practitioners. In this work, we argue that a fair assessment of optimizers' performance must take the computational cost of hyperparameter tuning into account, i.e., how easy it is to find good hyperparameter configurations using an automatic hyperparameter search. Evaluating a variety of optimizers on an extensive set of standard datasets and architectures, our results indicate that Adam is the most practical solution, particularly in low-budget scenarios.

We propose a new model for supervised learning to rank. In our model, the relevance labels are assumed to follow a categorical distribution whose probabilities are constructed based on a scoring function. We optimize the training objective with respect to the multivariate categorical variables with an unbiased and low-variance gradient estimator. Learning-to-rank methods can generally be categorized into pointwise, pairwise, and listwise approaches. Although our scoring function is pointwise, the proposed framework permits flexibility over the choice of the loss function. In our new model, the loss function need not be differentiable and can either be pointwise or listwise. Our proposed method achieves better or comparable results on two datasets compared with existing pairwise and listwise methods.

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated quantification of prediction uncertainty, while maintaining the expressive power of their deterministic counterpart. We assign Bayesian Neural Nets (BNNs) to both the drift and the diffusion terms of a Stochastic Differential Equation (SDE) that models the flow of the activation map in time. We infer the posterior on the BNN weights using a straightforward adaptation of Stochastic Gradient Langevin Dynamics (SGLD). We illustrate significantly improved stability on two synthetic time series prediction tasks and report better model fit on UCI regression benchmarks with our method when compared to its non-Bayesian counterpart.

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can be viewed as a specific discretisation scheme. The key idea is how to characterise the continuous dynamics of node representations, i.e. the derivatives of node representations, w.r.t. time. Inspired by existing diffusion-based methods on graphs (e.g. PageRank and epidemic models on social networks), we define the derivatives as a combination of the current node representations, the representations of neighbors, and the initial values of the nodes. We propose and analyse two possible dynamics on graphs---including each dimension of node representations (a.k.a. the feature channel) change independently or interact with each other---both with theoretical justification. The proposed continuous graph neural networks are robust to over-smoothing and hence allow us to build deeper networks, which in turn are able to capture the long-range dependencies between nodes. Experimental results on the task of node classification demonstrate the effectiveness of our proposed approach over competitive baselines.

Deep neural networks (DNNs) are poorly calibrated when trained in conventional ways. To improve confidence calibration of DNNs, we propose a novel training method, distance-based learning from errors (DBLE). DBLE bases its confidence estimation on distances in the representation space. In DBLE, we first adapt prototypical learning to train classification models. It yields a representation space where the distance between a test sample and its ground truth class center can calibrate the model's classification performance. At inference, however, these distances are not available due to the lack of ground truth labels. To circumvent this by inferring the distance for every test sample, we propose to train a confidence model jointly with the classification model. We integrate this into training by merely learning from mis-classified training samples, which we show to be highly beneficial for effective learning. On multiple datasets and DNN architectures, we demonstrate that DBLE outperforms alternative single-model confidence calibration approaches. DBLE also achieves comparable performance with computationally-expensive ensemble approaches with lower computational cost and lower number of parameters.

We propose a novel formulation of group fairness in the contextual multi-armed bandit (CMAB) setting. In the CMAB setting a sequential decision maker must at each time step choose an arm to pull from a finite set of arms after observing some context for each of the potential arm pulls. In our model arms are partitioned into two or more sensitive groups based on some protected feature (e.g., age, race, or socio-economic status). Despite the fact that there may be differences in expected payout between the groups, we may wish to ensure some form of fairness between picking arms from the various groups. In this work we explore two definitions of fairness: equal group probability, wherein the probability of pulling an arm from any of the protected groups is the same; and proportional parity, wherein the probability of choosing an arm from a particular group is proportional to the size of that group. We provide a novel algorithm that can accommodate these notions of fairness for an arbitrary number of groups, and provide bounds on the regret for our algorithm. We then validate our algorithm using synthetic data as well as two real-world datasets for intervention settings wherein we want to allocate resources fairly across protected groups.

We present a framework capable of tackilng the problem of continual object recognition in a setting which resembles that under whichhumans see and learn. This setting has a set of unique characteristics:it assumes an egocentric point-of-view bound to the needs of a singleperson, which implies a relatively low diversity of data and a coldstart with no data; it requires to operate in an open world, where newobjects can be encounteredat any time; supervision is scarce and hasto be solicited to the user, and completelyunsupervised recognitionof new objects should be possible. Note that this setting differs fromthe one addressed in the open world recognition literature, where supervised feedback is always requested to be able to incorporate newobjects. We propose a first solution to this problem in the form ofa memory-based incremental framework that is capable of storinginformation of each and any object it encounters, while using the supervision of the user to learn to discriminate between known and unknown objects. Our approach is based on four main features: the useof time and space persistence (i.e., the appearance of objects changesrelatively slowly), the use of similarity as the main driving principlefor object recognition and novelty detection, the progressive introduction of new objects in a developmental fashion and the selectiveelicitation of user feedback in an online active learning fashion. Experimental results show the feasibility of open world, generic objectrecognition, the ability to recognize, memorize and re-identify newobjects even in complete absence of user supervision, and the utilityof persistence and incrementality in boosting performance.

In this work, we estimate extreme sea surface temperature (SST) hotspots, i.e., high threshold exceedance regions, for the Red Sea, a vital region of high biodiversity. We analyze high-resolution satellite-derived SST data comprising daily measurements at 16703 grid cells across the Red Sea over the period 1985--2015. We propose a semiparametric Bayesian spatial mixed-effects linear model with a flexible mean structure to capture spatially-varying trend and seasonality, while the residual spatial variability is modeled through a Dirichlet process mixture (DPM) of low-rank spatial Student-$t$ processes (LTPs). By specifying cluster-specific parameters for each LTP mixture component, the bulk of the SST residuals influence tail inference and hotspot estimation only moderately. Our proposed model has a nonstationary mean, covariance and tail dependence, and posterior inference can be drawn efficiently through Gibbs sampling. In our application, we show that the proposed method outperforms some natural parametric and semiparametric alternatives. Moreover, we show how hotspots can be identified and we estimate extreme SST hotspots for the whole Red Sea, projected for the year 2100. The estimated 95\% credible region for joint high threshold exceedances include large areas covering major endangered coral reefs in the southern Red Sea.

We study risk of the minimum norm linear least squares estimator in when the number of parameters $d$ depends on $n$, and $\frac{d}{n} \rightarrow \infty$. We assume that data has an underlying low rank structure by restricting ourselves to spike covariance matrices, where a fixed finite number of eigenvalues grow with $n$ and are much larger than the rest of the eigenvalues, which are (asymptotically) in the same order. We show that in this setting risk of minimum norm least squares estimator vanishes in compare to risk of the null estimator. We give asymptotic and non asymptotic upper bounds for this risk, and also leverage the assumption of spike model to give an analysis of the bias that leads to tighter bounds in compare to previous works.

Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of Transformers. For one, we replace dot-product attention by one that uses locality-sensitive hashing, changing its complexity from O($L^2$) to O($L\log L$), where $L$ is the length of the sequence. Furthermore, we use reversible residual layers instead of the standard residuals, which allows storing activations only once in the training process instead of $N$ times, where $N$ is the number of layers. The resulting model, the Reformer, performs on par with Transformer models while being much more memory-efficient and much faster on long sequences.

Quantum effects are known to provide an advantage in particle transfer across networks. In order to achieve this advantage, requirements on both a graph type and a quantum system coherence must be found. Here we show that the process of finding these requirements can be automated by learning from simulated examples. The automation is done by using a convolutional neural network of a particular type that learns to understand with which network and under which coherence requirements quantum advantage is possible. Our machine learning approach is applied to study noisy quantum walks on cycle graphs of different sizes. We found that it is possible to predict the existence of quantum advantage for the entire decoherence parameter range, even for graphs outside of the training set. Our results are of importance for demonstration of advantage in quantum experiments and pave the way towards automating scientific research and discoveries.

We investigate how reinforcement learning can be used to train level-designing agents. This represents a new approach to procedural content generation in games, where level design is framed as a game, and the content generator itself is learned. By seeing the design problem as a sequential task, we can use reinforcement learning to learn how to take the next action so that the expected final level quality is maximized. This approach can be used when few or no examples exist to train from, and the trained generator is very fast. We investigate three different ways of transforming two-dimensional level design problems into Markov decision processes and apply these to three game environments.

Signal temporal logic (STL) is an expressive language to specify time-bound real-world robotic tasks and safety specifications. Recently, there has been an interest in learning optimal policies to satisfy STL specifications via reinforcement learning (RL). Learning to satisfy STL specifications often needs a sufficient length of state history to compute reward and the next action. The need for history results in exponential state-space growth for the learning problem. Thus the learning problem becomes computationally intractable for most real-world applications. In this paper, we propose a compact means to capture state history in a new augmented state-space representation. An approximation to the objective (maximizing probability of satisfaction) is proposed and solved for in the new augmented state-space. We show the performance bound of the approximate solution and compare it with the solution of an existing technique via simulations.

A recent body of work has focused on the theoretical study of neural networks at the regime of large width. Specifically, it was shown that training infinitely-wide and properly scaled vanilla ReLU networks using the L2 loss, is equivalent to kernel regression using the Neural Tangent Kernel (NTK), which is deterministic, and remains constant during training. In this work, we derive the form of the limiting kernel for architectures incorporating bypass connections, namely residual networks (ResNets), as well as to densely connected networks (DenseNets). In addition, we derive finite width and depth corrections for both cases. Our analysis reveals that deep practical residual architectures might operate much closer to the kernel regime'' than their vanilla counterparts: while in networks that do not use skip connections, convergence to the NTK requires one to fix depth, while increasing the layers' width. Our findings show that in ResNets, convergence to the NTK may occur when depth and width simultaneously tend to infinity, provided proper initialization. In DenseNets, however, convergence to the NTK as the width tend to infinity is guaranteed, at a rate that is independent of both depth and scale of the weights.

Background. Recently, In Italy the vaccination coverage for key immunizations, as MMR, has been declining, with measles outbreaks. In 2017, the Italian Government expanded the number of mandatory immunizations establishing penalties for families of unvaccinated children. During the 2018 elections campaign, immunization policy entered the political debate, with the government accusing oppositions of fuelling vaccine scepticism. A new government established in 2018 temporarily relaxed penalties and announced the introduction of flexibility.

Objectives and Methods. By a sentiment analysis on tweets posted in Italian during 2018, we aimed at (i) characterising the temporal flow of communication on vaccines, (ii) evaluating the usefulness of Twitter data for estimating vaccination parameters, and (iii) investigating whether the ambiguous political communication might have originated disorientation among the public.

Results. The population appeared to be mostly composed by "serial twitterers" tweeting about everything including vaccines. Tweets favourable to vaccination accounted for 75% of retained tweets, undecided for 14% and unfavourable for 11%. Twitter activity of the Italian public health institutions was negligible. After smoothing the temporal pattern, an up-and-down trend in the favourable proportion emerged, synchronized with the switch between governments, providing clear evidence of disorientation.

Conclusion. The reported evidence of disorientation documents that critical health topics, as immunization, should never be used for political consensus. This is especially true given the increasing role of online social media as information source, which might yield to social pressures eventually harmful for vaccine uptake, and is worsened by the lack of institutional presence on Twitter. This calls for efforts to contrast misinformation and the ensuing spread of hesitancy.

Large-scale nonconvex optimization problems are ubiquitous in modern machine learning, and among practitioners interested in solving them, Stochastic Gradient Descent (SGD) reigns supreme. We revisit the analysis of SGD in the nonconvex setting and propose a new variant of the recently introduced expected smoothness assumption which governs the behaviour of the second moment of the stochastic gradient. We show that our assumption is both more general and more reasonable than assumptions made in all prior work. Moreover, our results yield the optimal $\mathcal{O}(\varepsilon^{-4})$ rate for finding a stationary point of nonconvex smooth functions, and recover the optimal $\mathcal{O}(\varepsilon^{-1})$ rate for finding a global solution if the Polyak-{\L}ojasiewicz condition is satisfied. We compare against convergence rates under convexity and prove a theorem on the convergence of SGD under Quadratic Functional Growth and convexity, which might be of independent interest. Moreover, we perform our analysis in a framework which allows for a detailed study of the effects of a wide array of sampling strategies and minibatch sizes for finite-sum optimization problems. We corroborate our theoretical results with experiments on real and synthetic data.

Stochastic optimization algorithms, such as Stochastic Gradient Descent (SGD) and its variants, are mainstream methods for training deep networks in practice. However, the theoretical mechanism behind gradient noise still remains to be further investigated. Deep learning is known to find flat minima with a large neighboring region in parameter space from which each weight vector has similar small error. In this paper, we focus on a fundamental problem in deep learning, "How can deep learning usually find flat minima among so many minima?" To answer the question, we develop a density diffusion theory (DDT) for revealing the fundamental dynamical mechanism of SGD and deep learning. More specifically, we study how escape time from loss valleys to the outside of valleys depends on minima sharpness, gradient noise and hyperparameters. One of the most interesting findings is that stochastic gradient noise from SGD can help escape from sharp minima exponentially faster than flat minima, while white noise can only help escape from sharp minima polynomially faster than flat minima. We also find large-batch training requires exponentially many iterations to pass through sharp minima and find flat minima. We present direct empirical evidence supporting the proposed theoretical results.

We show a hardness result for random smoothing to achieve certified adversarial robustness against attacks in the $\ell_p$ ball of radius $\epsilon$ when $p>2$. Although random smoothing has been well understood for the $\ell_2$ case using the Gaussian distribution, much remains unknown concerning the existence of a noise distribution that works for the case of $p>2$. This has been posed as an open problem by Cohen et al. (2019) and includes many significant paradigms such as the $\ell_\infty$ threat model. In this work, we show that any noise distribution $\mathcal{D}$ over $\mathbb{R}^d$ that provides $\ell_p$ robustness with $p>2$ for all base classifiers must satisfy $\mathbb{E}\eta_i^2=\Omega(d^{1-2/p}\epsilon^2(1-\delta)/\delta^2)$ for 99% of the features (pixels) of vector $\eta$ drawn from $\mathcal{D}$, where $\epsilon$ is the robust radius and $\delta$ measures the score gap between the highest-scored class and the runner-up. Therefore, for high-dimensional images with pixel values bounded in $[0,255]$, the required noise will eventually dominate the useful information in the images, leading to trivial smoothed classifiers.

The latent spaces of typical GAN models often have semantically meaningful directions. Moving in these directions corresponds to human-interpretable image transformations, such as zooming or recoloring, enabling a more controllable generation process. However, the discovery of such directions is currently performed in a supervised manner, requiring human labels, pretrained models, or some form of self-supervision. These requirements can severely limit a range of directions existing approaches can discover. In this paper, we introduce an unsupervised method to identify interpretable directions in the latent space of a pretrained GAN model. By a simple model-agnostic procedure, we find directions corresponding to sensible semantic manipulations without any form of (self-)supervision. Furthermore, we reveal several non-trivial findings, which would be difficult to obtain by existing methods, e.g., a direction corresponding to background removal. As an immediate practical benefit of our work, we show how to exploit this finding to achieve a new state-of-the-art for the problem of saliency detection.

Graph deep learning has recently emerged as a powerful ML concept allowing to generalize successful deep neural architectures to non-Euclidean structured data. Such methods have shown promising results on a broad spectrum of applications ranging from social science, biomedicine, and particle physics to computer vision, graphics, and chemistry. One of the limitations of the majority of the current graph neural network architectures is that they are often restricted to the transductive setting and rely on the assumption that the underlying graph is known and fixed. In many settings, such as those arising in medical and healthcare applications, this assumption is not necessarily true since the graph may be noisy, partially- or even completely unknown, and one is thus interested in inferring it from the data. This is especially important in inductive settings when dealing with nodes not present in the graph at training time. Furthermore, sometimes such a graph itself may convey insights that are even more important than the downstream task. In this paper, we introduce Differentiable Graph Module (DGM), a learnable function predicting the edge probability in the graph relevant for the task, that can be combined with convolutional graph neural network layers and trained in an end-to-end fashion. We provide an extensive evaluation of applications from the domains of healthcare (disease prediction), brain imaging (gender and age prediction), computer graphics (3D point cloud segmentation), and computer vision (zero-shot learning). We show that our model provides a significant improvement over baselines both in transductive and inductive settings and achieves state-of-the-art results.

The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior distributions. However, one key limitation of existing normalizing flows is that they are restricted to the Euclidean space and are ill-equipped to model data with an underlying hierarchical structure. To address this fundamental limitation, we present the first extension of normalizing flows to hyperbolic spaces. We first elevate normalizing flows to hyperbolic spaces using coupling transforms defined on the tangent bundle, termed Tangent Coupling ($\mathcal{TC}$). We further introduce Wrapped Hyperboloid Coupling ($\mathcal{W}\mathbb{H}C$), a fully invertible and learnable transformation that explicitly utilizes the geometric structure of hyperbolic spaces, allowing for expressive posteriors while being efficient to sample from. We demonstrate the efficacy of our novel normalizing flow over hyperbolic VAEs and Euclidean normalizing flows. Our approach achieves improved performance on density estimation, as well as reconstruction of real-world graph data, which exhibit a hierarchical structure. Finally, we show that our approach can be used to power a generative model over hierarchical data using hyperbolic latent variables.

The top-k operation, i.e., finding the k largest or smallest elements from a collection of scores, is an important model component, which is widely used in information retrieval, machine learning, and data mining. However, if the top-k operation is implemented in an algorithmic way, e.g., using bubble algorithm, the resulting model cannot be trained in an end-to-end way using prevalent gradient descent algorithms. This is because these implementations typically involve swapping indices, whose gradient cannot be computed. Moreover, the corresponding mapping from the input scores to the indicator vector of whether this element belongs to the top-k set is essentially discontinuous. To address the issue, we propose a smoothed approximation, namely the SOFT (Scalable Optimal transport-based diFferenTiable) top-k operator. Specifically, our SOFT top-k operator approximates the output of the top-k operation as the solution of an Entropic Optimal Transport (EOT) problem. The gradient of the SOFT operator can then be efficiently approximated based on the optimality conditions of EOT problem. We apply the proposed operator to the k-nearest neighbors and beam search algorithms, and demonstrate improved performance.

Testing automotive mechatronic systems partly uses the software-in-the-loop approach, where systematically covering inputs of the system-under-test remains a major challenge. In current practice, there are two major techniques of input stimulation. One approach is to craft input sequences which eases control and feedback of the test process but falls short of exposing the system to realistic scenarios. The other is to replay sequences recorded from field operations which accounts for reality but requires collecting a well-labeled dataset of sufficient capacity for widespread use, which is expensive. This work applies the well-known unsupervised learning framework of Generative Adversarial Networks (GAN) to learn an unlabeled dataset of recorded in-vehicle signals and uses it for generation of synthetic input stimuli. Additionally, a metric-based linear interpolation algorithm is demonstrated, which guarantees that generated stimuli follow a customizable similarity relationship with specified references. This combination of techniques enables controlled generation of a rich range of meaningful and realistic input patterns, improving virtual test coverage and reducing the need for expensive field tests.

The information bottleneck principle provides an information-theoretic method for representation learning, by training an encoder to retain all information which is relevant for predicting the label while minimizing the amount of other, excess information in the representation. The original formulation, however, requires labeled data to identify the superfluous information. In this work, we extend this ability to the multi-view unsupervised setting, where two views of the same underlying entity are provided but the label is unknown. This enables us to identify superfluous information as that not shared by both views. A theoretical analysis leads to the definition of a new multi-view model that produces state-of-the-art results on the Sketchy dataset and label-limited versions of the MIR-Flickr dataset. We also extend our theory to the single-view setting by taking advantage of standard data augmentation techniques, empirically showing better generalization capabilities when compared to common unsupervised approaches for representation learning.

Stochastic networks based on random point sets as nodes have attracted considerable interest in many applications, particularly in communication networks, including wireless sensor networks, peer-to-peer networks and so on. The study of such networks generally requires the nodes to be independently and uniformly distributed as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate the stochastic geometry of networks obtained from \textit{directed spanning forests} (DSF) based on randomly perturbed lattices, which have desirable statistical properties as a models of spatially dependent point fields. In the regime of low disorder, we show in 2D and 3D that the DSF almost surely consists of a single tree. In 2D, we further establish that the DSF, as a collection of paths, converges under diffusive scaling to the Brownian web.