Related papers: Outlier-robust sparse/low-rank least-squares regre…

We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…

We study the problem of high-dimensional sparse mean estimation in the presence of an $\epsilon$-fraction of adversarial outliers. Prior work obtained sample and computationally efficient algorithms for this task for identity-covariance…

We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…

Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…

Reduced rank regression (RRR) is a fundamental tool for modeling multiple responses through low-dimensional latent structures, offering both interpretability and strong predictive performance in high-dimensional settings. Classical RRR…

We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…

We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…

We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

We tackle estimating sparse coefficients in a linear regression when the covariates are sampled from an $L$-subexponential random vector. This vector belongs to a class of distributions that exhibit heavier tails than Gaussian random…

Consider the problem of simultaneous estimation of location and variance matrix under Huber's contaminated Gaussian model. First, we study minimum $f$-divergence estimation at the population level, corresponding to a generative adversarial…

We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…

Robust low-rank approximation under row-wise adversarial corruption can be achieved with a single pass, randomized procedure that detects and removes outlier rows by thresholding their projected norms. We propose a scalable, non-iterative…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…