Related papers: How Hard Is Robust Mean Estimation?
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…
Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a…
Our focus is on robust recovery algorithms in statistical linear inverse problem. We consider two recovery routines - the much studied linear estimate originating from Kuks and Olman [42] and polyhedral estimate introduced in [37]. It was…
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…
We consider a fundamental problem in unsupervised learning called \emph{subspace recovery}: given a collection of $m$ points in $\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$…
Developing simple, sample-efficient learning algorithms for robust classification is a pressing issue in today's tech-dominated world, and current theoretical techniques requiring exponential sample complexity and complicated improper…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted…
Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is…
Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and…
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
The $k$-of-$n$ testing problem involves performing $n$ independent tests sequentially, in order to determine whether/not at least $k$ tests pass. The objective is to minimize the expected cost of testing. This is a fundamental and…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…
This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…
We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…
Adversarially robust learning aims to design algorithms that are robust to small adversarial perturbations on input variables. Beyond the existing studies on the predictive performance to adversarial samples, our goal is to understand…
Budgeted uncertainty sets have been established as a major influence on uncertainty modeling for robust optimization problems. A drawback of such sets is that the budget constraint only restricts the global amount of cost increase that can…