Big data can easily be contaminated by outliers or contain variables with heavy-tailed
distributions, which makes many conventional methods inadequate. To address this …

Supplementary material to “Estimation bounds and sharp oracle inequalities of regularized
procedures with Lipschitz loss functions”. Section 6 gives the proof of the main results …

Concentration of tempered posteriors and of their variational approximations Page 1 The
Annals of Statistics 2020, Vol. 48, No. 3, 1475–1497 https://doi.org/10.1214/19-AOS1855 © …

The robustication parameter, which balances bias and robustness, plays a critical role in the
construction of subGaussian estimators for heavy-tailed and/or skewed data. Although the …

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor,
where the low-rank tensor often captures the multi-way principal components and the sparse …

Nonparametric regression subject to convexity or concavity constraints is increasingly
popular in economics, finance, operations research, machine learning, and statistics …

This article studies noisy low-rank matrix completion in the presence of heavy-tailed and
possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a …

In this paper we consider high-dimensional multiclass classification by sparse multinomial
logistic regression. We propose first a feature selection procedure based on penalized …

These notes gather some results dealing with robustness issues in statistical learning. Most
of the results lie within the framework introduced by Vapnik [58], see also [44]. Given a …

These notes gather recent results on robust statistical learning theory. The goal is to stress
the main principles underlying the construction and theoretical analysis of these estimators …