Related papers: Universal Robust Regression via Maximum Mean Discr…

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…

High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced…

We consider robust estimation when outputs are adversarially contaminated. Nguyen and Tran (2012) proposed an extended Lasso for robust parameter estimation and then they showed the convergence rate of the estimation error. Recently,…

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…

Multivariate linear regression is a fundamental statistical task, but classical estimators such as ordinary least squares are highly sensitive to outliers. These may occur as casewise outliers that affect entire observations, or as outlying…

Robust scatter estimation is a fundamental task in statistics. The recent discovery on the connection between robust estimation and generative adversarial nets (GANs) by Gao et al. (2018) suggests that it is possible to compute depth-like…

The problem of identifying the most discriminating features when performing supervised learning has been extensively investigated. In particular, several methods for variable selection in model-based classification have been proposed.…

We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…

For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…

Data on rates, percentages or proportions arise frequently in many different applied disciplines like medical biology, health care, psychology and several others. In this paper, we develop a robust inference procedure for the beta…

High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those…

In today's era of big data, robust least-squares regression becomes a more challenging problem when considering the adversarial corruption along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer…

We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…

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…

We study the robust mean estimation problem in high dimensions, where $\alpha <0.5$ fraction of the data points can be arbitrarily corrupted. Motivated by compressive sensing, we formulate the robust mean estimation problem as the…

Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber--White sandwich estimator. The sandwich estimator is known to provide asymptotically…

Missing data is frequently encountered in many areas of statistics. Propensity score weighting is a popular method for handling missing data. The propensity score method employs a response propensity model, but correct specification of the…