Related papers: Bayesian Robustness: A Nonasymptotic Viewpoint
Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…
Robustness in AI systems refers to their ability to maintain reliable and accurate performance under various conditions, including out-of-distribution (OOD) samples, adversarial attacks, and environmental changes. This is crucial in…
We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations. Given a compact set of input points $T \subseteq \mathbb{R}^m$ and a set of output points $S \subseteq \mathbb{R}^n$,…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based…
We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…
Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is…
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…
It has recently been discovered that the conclusions of many highly influential econometrics studies can be overturned by removing a very small fraction of their samples (often less than $0.5\%$). These conclusions are typically based on…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
This paper proposes a new Bayesian approach for analysing moment condition models in the situation where the data may be contaminated by outliers. The approach builds upon the foundations developed by Schennach (2005) who proposed the…
We introduce the $\widetilde{\rho}$-posterior, a modified version of the $\rho$-posterior, obtained by replacing the supremum over competitor parameters with a softmax aggregation. This modification allows a PAC-Bayesian analysis of the…
Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…
We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…
This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection. The resulting algorithm has key advantages over previous work: it provides provable robustness by leveraging the generalised Bayesian…
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a…
The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…