Related papers: Outlier-Robust Sparse Mean Estimation for Heavy-Ta…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

We develop efficient algorithms for estimating low-degree moments of unknown distributions in the presence of adversarial outliers. The guarantees of our algorithms improve in many cases significantly over the best previous ones, obtained…

In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…

A Gaussian measurement error assumption, i.e., an assumption that the data are observed up to Gaussian noise, can bias any parameter estimation in the presence of outliers. A heavy tailed error assumption based on Student's t distribution…

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…

We study the distributed stochastic optimization (DSO) problem under a heavy-tailed noise condition by utilizing a multi-agent system. Despite the extensive research on DSO algorithms used to solve DSO problems under light-tailed noise…

We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…

Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was…

This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…

In this work we study high probability bounds for stochastic subgradient methods under heavy tailed noise. In this setting the noise is only assumed to have finite variance as opposed to a sub-Gaussian distribution for which it is known…

We study the classic $k$-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by…

We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to…

This paper investigates the theoretical underpinnings of two fundamental statistical inference problems, the construction of confidence sets and large-scale simultaneous hypothesis testing, in the presence of heavy-tailed data. With…

High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Pulsar-timing datasets have been analyzed with great success using probabilistic treatments based on Gaussian distributions, with applications ranging from studies of neutron-star structure to tests of general relativity and searches for…

We consider the problem of constructing a least conservative estimator of the expected value $\mu$ of a non-negative heavy-tailed random variable. We require that the probability of overestimating the expected value $\mu$ is kept…

The large variety of functions encountered in nonparametric statistics, calls for methods that are flexible enough to achieve optimal or near-optimal performance over a wide variety of functional classes, such as Besov balls, as well as…

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…