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In multi-objective decision planning and learning, much attention is paid toproducing optimal solution sets that contain an optimal policy for everypossible user preference profile. We argue that the step that follows, i.e,determining which policy to execute by maximising the user's intrinsic...

Conditional Kendall's tau is a measure of dependence between two randomvariables, conditionally on some covariates. We study nonparametric estimatorsof such quantities using kernel smoothing techniques. Then, we assume aregression-type relationship between conditional Kendall's tau and covariates,in...

In this paper, we consider the estimation of a change-point for possiblyhigh-dimensional data in a Gaussian model, using a k-means method. We provethat, up to a logarithmic term, this change-point estimator has a minimax rateof convergence. Then, considering the case of sparse data, with a...

Sparse subspace clustering (SSC) is one of the current state-of-the-artmethod for partitioning data points into the union of subspaces, with strongtheoretical guarantees. However, it is not practical for large data sets as itrequires solving a LASSO problem for each data point, where the number...

Generating video frames that accurately predict future world states ischallenging. Existing approaches either fail to capture the full distributionof outcomes, or yield blurry generations, or both. In this paper we introducean unsupervised video generation model that learns a prior model of...

In this paper we propose a new approach for sequential monitoring of aparameter of a $d$-dimensional time series. We consider a closed-end-method,which is motivated by the likelihood ratio test principle and compare the newmethod with two alternative procedures. We also incorporate self...

The roles played by learning and memorization represent an important topic indeep learning research. Recent work on this subject has shown that theoptimization behavior of DNNs trained on shuffled labels is qualitativelydifferent from DNNs trained with real labels. Here, we propose a...

A central concern of network operators is to estimate the probability of anincident that affects a significant part and thus may yield to a breakdown. Weanswer this question by modeling how a failure of either a node or an edge willaffect the rest of the network using percolation theory. Our model...

We consider in this paper the problem of sampling a high-dimensionalprobability distribution $\pi$ having a density \wrt\ the Lebesgue measure on$\mathbb{R}^d$, known up to a normalization factor $x \mapsto \pi(x)=\mathrm{e}^{-U(x)}/\int_{\mathbb{R}^d} \mathrm{e}^{-U(y)} \mathrm{d}y$. Suchproblem...

Vote-boosting is a sequential ensemble learning method in which theindividual classifiers are built on different weighted versions of the trainingdata. To build a new classifier, the weight of each training instance isdetermined in terms of the degree of disagreement among the current...

Recurrent neural network (RNN)'s architecture is a key factor influencing itsperformance. We propose algorithms to optimize hidden sizes under running timeconstraint. We convert the discrete optimization into a subset selectionproblem. By novel transformations, the objective function becomes...

Deep learning models' architectures, including depth and width, are keyfactors influencing models' performance, such as test accuracy and computationtime. This paper solves two problems: given computation time budget, choose anarchitecture to maximize accuracy, and given accuracy requirement, choose...

Stein's method for measuring convergence to a continuous target distributionrelies on an operator characterizing the target and Stein factor bounds on thesolutions of an associated differential equation. While such operators andbounds are readily available for a diversity of univariate targets...

This paper studies models in which hypothesis tests have trivial power, thatis, power smaller than size. This testing impossibility, or impossibility typeA, arises when any alternative is not distinguishable from the null. We alsostudy settings where it is impossible to have almost surely bounded...

The probability density quantile (pdQ) carries essential informationregarding shape and tail behavior of a location-scale family. Convergence ofrepeated applications of the pdQ mapping to the uniform distribution isinvestigated and new fixed point theorems are established. The Kullback...

Inferring the correct answers to binary tasks based on multiple noisy answersin an unsupervised manner has emerged as the canonical question for micro-taskcrowdsourcing or more generally aggregating opinions. In graphon estimation,one is interested in estimating edge intensities or probabilities...

Many recent advances in large scale probabilistic inference rely onvariational methods. The success of variational approaches depends on (i)formulating a flexible parametric family of distributions, and (ii) optimizingthe parameters to find the member of this family that most closely approximatesthe...

We study a deep linear network expressed under the form of a matrixfactorization problem. It takes as input a matrix $X$ obtained by multiplying$K$ matrices (called factors and corresponding to the action of a layer). Eachfactor is obtained by applying a fixed linear operator to a vector...

Many medical decisions involve the use of dynamic information collected onindividual patients toward predicting likely transitions in their future healthstatus. If accurate predictions are developed, then a prognostic mode canidentify patients at greatest risk for future adverse events, and may be...

Convolutional neural networks (CNNs) have been successfully applied to manyrecognition and learning tasks using a universal recipe; training a deep modelon a very large dataset of supervised examples. However, this approach israther restrictive in practice since collecting a large set of labeled...