Related papers: High-dimensional robust regression under heavy-tai…

As one of the triumphs and milestones of robust statistics, Huber regression plays an important role in robust inference and estimation. It has also been finding a great variety of applications in machine learning. In a parametric setup, it…

Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…

This paper introduces a loss-based generalized Bayesian methodology for high-dimensional robust regression with serially correlated errors and predictors. The proposed framework employs a novel scaled pseudo-Huber (SPH) loss function, which…

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…

This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against…

Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to `multiplicative noise', even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have…

A large body of work in the statistics and computer science communities dating back to Huber (Huber, 1960) has led to statistically and computationally efficient outlier-robust estimators. Two particular outlier models have received…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

In this paper, we study the properties of robust nonparametric estimation using deep neural networks for regression models with heavy tailed error distributions. We establish the non-asymptotic error bounds for a class of robust…

Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…

In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of…

We consider the problem of sparsity-constrained $M$-estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the $k$-sparse, high-dimensional regime…

We consider distributed recursive estimation of consensus+innovations type in the presence of heavy-tailed sensing and communication noises. We allow that the sensing and communication noises are mutually correlated while independent…

Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…

In recent years, various notions of capacity and complexity have been proposed for characterizing the generalization properties of stochastic gradient descent (SGD) in deep learning. Some of the popular notions that correlate well with the…