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We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated. Several computationally efficient estimators have been proposed for the simpler setting…

Statistics Theory · Mathematics 2021-05-18 Ankit Pensia , Varun Jog , Po-Ling Loh

We begin the study of list-decodable linear regression using batches. In this setting only an $\alpha \in (0,1]$ fraction of the batches are genuine. Each genuine batch contains $\ge n$ i.i.d. samples from a common unknown distribution and…

Machine Learning · Computer Science 2022-11-24 Abhimanyu Das , Ayush Jain , Weihao Kong , Rajat Sen

We study random design linear regression with no assumptions on the distribution of the covariates and with a heavy-tailed response variable. In this distribution-free regression setting, we show that boundedness of the conditional second…

Statistics Theory · Mathematics 2022-02-25 Jaouad Mourtada , Tomas Vaškevičius , Nikita Zhivotovskiy

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…

Statistics Theory · Mathematics 2010-11-10 Victor Konev , Serguei Pergamenchtchikov

We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…

Statistics Theory · Mathematics 2009-08-21 Emmanuel J. Candès , Yaniv Plan

A powerful concept behind much of the recent progress in machine learning is the extraction of common features across data from heterogeneous sources or tasks. Intuitively, using all of one's data to learn a common representation function…

Machine Learning · Statistics 2024-10-15 Thomas T. C. K. Zhang , Leonardo F. Toso , James Anderson , Nikolai Matni

We study the Gaussian Process regression model in the context of training data with noise in both input and output. The presence of two sources of noise makes the task of learning accurate predictive models extremely challenging. However,…

Machine Learning · Statistics 2015-07-03 Cuong Tran , Vladimir Pavlovic , Robert Kopp

Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least…

Machine Learning · Computer Science 2018-10-08 Michał Dereziński , Manfred K. Warmuth , Daniel Hsu

The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection,…

Statistics Theory · Mathematics 2007-07-13 Martin J. Wainwright

We study robust high-dimensional sparse regression under finite-variance heavy-tailed noise, epsilon-contamination, and alpha-mixing dependence via two subsampling estimators: Adaptive Importance Sampling (AIS) and Stratified Sub-sampling…

Statistics Theory · Mathematics 2026-03-11 Prateek Mittal , Joohi Chauhan

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…

Machine Learning · Statistics 2012-12-04 Xun Huan , Youssef M. Marzouk

Neural processes amortize Gaussian process inference, replacing the exact $O(n^3)$ posterior with a learned $O(n)$ map from context sets to predictive distributions. For a class of latent neural processes, we bound the Kullback--Leibler…

Machine Learning · Computer Science 2026-05-22 Robin Young

Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is…

Methodology · Statistics 2021-03-02 Eva Cantoni , Xavier de Luna

We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…

Instrumentation and Methods for Astrophysics · Physics 2011-10-18 Niels Oppermann , Georg Robbers , Torsten A. Ensslin

We consider in this paper a contamined regression model where the distribution of the contaminating component is known when the Eu- clidean parameters of the regression model, the noise distribution, the contamination ratio and the…

Statistics Theory · Mathematics 2011-11-10 Pierre Vandekerkhove

We revisit heavy-tailed corrupted least-squares linear regression assuming to have a corrupted $n$-sized label-feature sample of at most $\epsilon n$ arbitrary outliers. We wish to estimate a $p$-dimensional parameter $b^*$ given such…

Statistics Theory · Mathematics 2022-09-08 Roberto I. Oliveira , Zoraida F. Rico , Philip Thompson

Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…

Methodology · Statistics 2026-05-01 Jing Ouyang , Chengyu Cui , Yunxiao Chen , Kean Ming Tan , Gongjun Xu

We investigate a problem estimating coefficients of linear regression under sparsity assumption when covariates and noises are sampled from heavy tailed distributions. Additionally, we consider the situation where not only covariates and…

Machine Learning · Statistics 2024-08-05 Takeyuki Sasai , Hironori Fujisawa

We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and…

Information Theory · Computer Science 2015-09-16 Alyson K. Fletcher , Sundeep Rangan

We consider a sparse linear regression model Y=X\beta^{*}+W where X has a Gaussian entries, W is the noise vector with mean zero Gaussian entries, and \beta^{*} is a binary vector with support size (sparsity) k. Using a novel conditional…

Machine Learning · Statistics 2019-09-26 David Gamarnik , Ilias Zadik