Related papers: Robust estimations from distribution structures: I…

K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a…

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…

Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…

Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious…

Many standard estimators such as several maximum likelihood estimators or the empirical estimator for any law-invariant convex risk measure are not (qualitatively) robust in the classical sense. However, these estimators may nevertheless…

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…

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete)…

This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper…

Given a dataset an outlier can be defined as an observation that it is unlikely to follow the statistical properties of the majority of the data. Computation of the location estimate of is fundamental in data analysis, and it is well known…

With the tremendous success of deep learning in visual tasks, the representations extracted from intermediate layers of learned models, that is, deep features, attract much attention of researchers. Previous empirical analysis shows that…

Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…

Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data - data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where,…

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory…

Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…

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 consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (i) models should be designed to accommodate deductibles, policy limits, and coinsurance factors, (ii)…

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…