Related papers: Robust dimension-free Gram operator estimates

In many applications we seek to maximize an expectation with respect to a distribution over discrete variables. Estimating gradients of such objectives with respect to the distribution parameters is a challenging problem. We analyze…

Robust implementable output regulator design approaches are studied for general linear continuous-time \mbox{systems} with periodically sampled measurements, consisting of both the regulation errors and extra measurements that are generally…

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…

Training large-scale mixture of experts models efficiently on modern hardware requires assigning datapoints in a batch to different experts, each with a limited capacity. Recently proposed assignment procedures lack a probabilistic…

We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…

This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions,…

This paper investigates calibration of sensor arrays in the radio astronomy context. Current and future radio telescopes require computationally efficient algorithms to overcome the new technical challenges as large collecting area, wide…

We derive an equilibrated a posteriori error estimator for the space (semi) discretization of the scalar wave equation by finite elements. In the idealized setting where time discretization is ignored and the simulation time is large, we…

We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal…

In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in…

We formalize notions of robustness for composite estimators via the notion of a breakdown point. A composite estimator successively applies two (or more) estimators: on data decomposed into disjoint parts, it applies the first estimator on…

A stylized feature of high-dimensional data is that many variables have heavy tails, and robust statistical inference is critical for valid large-scale statistical inference. Yet, the existing developments such as Winsorization,…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…

We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…

State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…

We derive a posteriori error estimates for a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation. The a posteriori bound is obtained by a splitting of the equation into a linear stochastic partial…

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression…