Related papers: Robust and efficient mean estimation: an approach …
The topic of robustness is experiencing a resurgence of interest in the statistical and machine learning communities. In particular, robust algorithms making use of the so-called median of means estimator were shown to satisfy strong…
Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the…
We develop a procedure that transforms any asymptotically normal estimator into an asymptotically normal estimator whose distribution is robust to arbitrary data contamination. More generally, our procedure transforms any estimator whose…
Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…
The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a…
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a…
We propose an estimator for the mean of a random vector in $\mathbb{R}^d$ that can be computed in time $O(n^4+n^2d)$ for $n$ i.i.d.~samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the…
This paper investigates asymptotic properties of algorithms that can be viewed as robust analogues of the classical empirical risk minimization. These strategies are based on replacing the usual empirical average by a robust proxy of the…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
We present \textit{universal} estimators for the statistical mean, variance, and scale (in particular, the interquartile range) under pure differential privacy. These estimators are universal in the sense that they work on an arbitrary,…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…
Robust estimation approaches are of fundamental importance for statistical modelling. To reduce susceptibility to outliers, we propose a robust estimation procedure with t-process under functional ANOVA model. Besides common mean structure…
As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…
Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious…
We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…