Related papers: Robust Gradient Descent Estimation for Tensor Mode…

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…

We study high-probability convergence guarantees of learning on streaming data in the presence of heavy-tailed noise. In the proposed scenario, the model is updated in an online fashion, as new information is observed, without storing any…

We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…

In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any estimates achieving some attainable error rate, we develop the…

We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded…

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…

In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

Chance-constrained motion planning requires uncertainty in dynamics to be propagated into uncertainty in state. When nonlinear models are used, Gaussian assumptions on the state distribution do not necessarily apply since almost all random…

Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…

Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is…

We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between…

Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

Multiview latent-variable models provide a fundamental framework for discrete data analysis, with applications to latent structure models, topic models, and mixtures of product distributions. In the discrete setting, the joint distribution…

In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of…

This paper considers the problem of asynchronous stochastic nonconvex optimization with heavy-tailed gradient noise and arbitrarily heterogeneous computation times across workers. We propose an asynchronous normalized stochastic gradient…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…