Related papers: Finite sample breakdown point of Tukey's halfspace…
In this paper, we study the stability and convergence of some general quadratic semimartingales. Motivated by financial applications, we study simultaneously the semimartingale and its opposite. Their characterization and integrability…
We present the results from a numerical investigation using the finite element method to study the buckling strength of near-perfect spherical shells containing a single, localized, Gaussian-dimple defect whose profile is systematically…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…
We prove a generalization of the hyperplane inequality for intersection bodies, where volume is replaced by an arbitrary measure $\mu$ with even continuous density and sections are of arbitrary dimension $n-k,\ 1\le k <n.$ If $K$ is a…
We revisit the problem of estimating the mean of a high-dimensional distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. When $\varepsilon$ is at most some sufficiently small constant, previous works can…
We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators achieve optimal rates of convergence under minimal assumptions on the dataset.…
Several recent works encourage the use of a Bayesian framework when assessing performance and fairness metrics of a classification algorithm in a supervised setting. We propose the Uncertainty Matters (UM) framework that generalizes a…
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…
We propose a new distribution, called the soft tMVN distribution, which provides a smooth approximation to the truncated multivariate normal (tMVN) distribution with linear constraints. An efficient blocked Gibbs sampler is developed to…
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose…
The consistency of Fr\'echet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies…
\We introduce the horospherical depth, an intrinsic notion of statistical depth on Hadamard manifolds, and define the Busemann median as the set of its maximizers. The construction exploits the fact that the linear functionals appearing in…
We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to…
The concept of breakdown point was introduced by Hampel [Ph.D. dissertation (1968), Univ. California, Berkeley; Ann. Math. Statist. 42 (1971) 1887-1896] and developed further by, among others, Huber [Robust Statistics (1981). Wiley, New…
Motivated by the widely used geometric median-of-means estimator in machine learning, this paper studies statistical inference for ultrahigh dimensionality location parameter based on the sample spatial median under a general multivariate…
The theory underlying robust distributed learning algorithms, designed to resist adversarial machines, matches empirical observations when data is homogeneous. Under data heterogeneity however, which is the norm in practical scenarios,…
A robust mean value is often a good alternative to the standard mean value when dealing with data containing many outliers. An efficient method for samples of one-dimensional features and the truncated quadratic error norm is presented and…
In this article we suggest a new statistical approach considering survival heterogeneity as a breakpoint model in an ordered sequence of time to event variables. The survival responses need to be ordered according to a numerical covariate.…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…