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Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…

Statistics Theory · Mathematics 2021-06-02 Mehmet Siddik Cadirci , Dafydd Evans , Nikolai Leonenko , Oleg Seleznjev

This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the \emph{expected} rate of the sensor-detector link is constrained. Unlike for the well-known…

Information Theory · Computer Science 2019-10-21 Sadaf Salehkalaibar , Michele Wigger

We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a…

Data Structures and Algorithms · Computer Science 2025-09-23 Hadley Black , Christopher Ye

In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the…

Information Theory · Computer Science 2022-07-07 Minh Thanh Vu

Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…

Data Structures and Algorithms · Computer Science 2023-04-05 Renato Ferreira Pinto , Nathaniel Harms

We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…

Machine Learning · Computer Science 2012-10-16 Maayan Harel , Shie Mannor

Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative.…

Statistics Theory · Mathematics 2019-09-10 Tong Li , Ming Yuan

We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…

Statistics Theory · Mathematics 2018-05-24 Guy Bresler , Dheeraj Nagaraj

We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results…

Quantum Physics · Physics 2012-01-30 G. M. Bosyk , M. Portesi , A. Plastino

This paper develops a statistical framework for goodness-of-fit testing of volatility functions in McKean-Vlasov stochastic differential equations, which describe large systems of interacting particles with distribution-dependent dynamics.…

Methodology · Statistics 2025-10-15 Akram Heidari , Mark Podolskij

We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…

Data Structures and Algorithms · Computer Science 2026-05-25 Clément L. Canonne , Yash Pote , Jonathan Scarlett , Joy Qiping Yang

We consider the goodness of fit testing problem for stochastic differential equation with small diffiusion coefficient. The basic hypothesis is always simple and it is described by the known trend coefficient. We propose several tests of…

Statistics Theory · Mathematics 2009-03-27 Yury A. Kutoyants

We study finite-sample inference for the trade-off function of two unknown probability distributions, the function that traces the optimal type I/type II error frontier in binary testing. Given samples from distributions $P$ and $Q$, we…

Statistics Theory · Mathematics 2026-05-12 Kaining Shi , Qiaosen Wang , Cong Ma

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

Statistics Theory · Mathematics 2018-03-13 Nikita Zhivotovskiy

In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…

Information Theory · Computer Science 2026-04-21 Arick Grootveld , Biao Chen , Venkata Gandikota

The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well…

Signal Processing · Electrical Eng. & Systems 2023-08-08 Zhongchang Sun , Shaofeng Zou

We study a variant of the simple hypothesis testing problem where observed samples do not necessarily come from either of the specified distributions, but rather from a close variant of them. In this setting, we require a test that is…

Statistics Theory · Mathematics 2026-04-21 Eeshan Modak , Sivaraman Balakrishnan , Ananda Theertha Suresh

We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the…

In this paper we propose a nonparametric graphical test based on optimal matching, for assessing the equality of multiple unknown multivariate probability distributions. Our procedure pools the data from the different classes to create a…

We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…

Methodology · Statistics 2021-12-07 Kyoungjae Lee , Kisung You , Lizhen Lin