Related papers: Minimax Robust Detection: Classic Results and Rece…
In this paper, we further develop the approach, originating in [GJN], to "computation-friendly" hypothesis testing via Convex Programming. Most of the existing results on hypothesis testing aim to quantify in a closed analytic form…
This paper considers an ML inspired approach to hypothesis testing known as classifier/classification-accuracy testing ($\mathsf{CAT}$). In $\mathsf{CAT}$, one first trains a classifier by feeding it labeled synthetic samples generated by…
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…
Softmax distributions are widely used in machine learning, including Large Language Models (LLMs), where the attention unit uses softmax distributions. We abstract the attention unit as the softmax model, where given a vector input, the…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…
Multi-target tracking (MTT) serves as a cornerstone technology in information fusion, yet faces significant challenges in robustness and efficiency when dealing with model uncertainties, clutter interference, and target interactions.…
We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates…
A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior,…
A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
Sequential multi-class diagnosis, also known as multi-hypothesis testing, is a classical sequential decision problem with broad applications. However, the optimal solution remains, in general, unknown as the dynamic program suffers from the…
The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from…
We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…
In this paper, two types of linear estimators are considered for three related estimation problems involving set-theoretic uncertainty pertaining to $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ balls of frequency-responses. The problems at…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
The problem of identifying the most discriminating features when performing supervised learning has been extensively investigated. In particular, several methods for variable selection in model-based classification have been proposed.…
We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via minimization of a suitable (empirical) version of the…
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…
Recently, the robustness of deep learning models has received widespread attention, and various methods for improving model robustness have been proposed, including adversarial training, model architecture modification, design of loss…