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Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…

Machine Learning · Computer Science 2024-11-19 Sutanu Gayen , Sanket Kale , Sayantan Sen

A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…

High Energy Physics - Phenomenology · Physics 2013-09-30 Fabio Siringo

We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…

Statistics Theory · Mathematics 2020-10-23 F. Richard Guo , Thomas S. Richardson

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

In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a…

Probability · Mathematics 2007-06-07 Elizabeth Meckes

In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…

Data Structures and Algorithms · Computer Science 2016-05-10 Ilias Diakonikolas , Daniel M. Kane

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Statistics Theory · Mathematics 2022-11-15 Loris Michel , Jeffrey Näf , Nicolai Meinshausen

The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…

Probability · Mathematics 2019-03-20 Georg Berschneider , Björn Böttcher

The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…

Statistics Theory · Mathematics 2014-12-30 Dayu Huang , Sean Meyn

The paper studies distributed binary hypothesis testing over a two-hop relay network where both the relay and the receiver decide on the hypothesis. Both communication links are subject to expected rate constraints, which differs from the…

Information Theory · Computer Science 2021-05-28 Mustapha Hamad , Michèle Wigger , Mireille Sarkiss

In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…

Statistics Theory · Mathematics 2019-01-14 Anupam Kundu , Subir Kumar Bhandari

We study two-sample variable selection: identifying variables that discriminate between the distributions of two sets of data vectors. Such variables help scientists understand the mechanisms behind dataset discrepancies. Although…

Machine Learning · Statistics 2025-11-06 Kensuke Mitsuzawa , Motonobu Kanagawa , Stefano Bortoli , Margherita Grossi , Paolo Papotti

We consider the hypothesis testing problem of detecting conditional dependence, with a focus on high-dimensional feature spaces. Our contribution is a new test statistic based on samples from a generative adversarial network designed to…

Machine Learning · Statistics 2019-12-20 Alexis Bellot , Mihaela van der Schaar

We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay…

Statistics Theory · Mathematics 2020-01-29 Sayar Karmakar , Wei Biao Wu

Correlation analysis is a fundamental step in uncovering meaningful insights from complex datasets. In this paper, we study the problem of detecting correlations between two random graphs following the Gaussian Wigner model with unlabeled…

Statistics Theory · Mathematics 2025-05-21 Dong Huang , Pengkun Yang

Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian…

Machine Learning · Statistics 2009-10-02 Philipp Hennig

We study the problem of mismatched likelihood ratio test. We analyze the type-\RNum{1} and \RNum{2} error exponents when the actual distributions generating the observation are different from the distributions used in the test. We derive…

Information Theory · Computer Science 2020-01-14 Parham Boroumand , Albert Guillen i Fabregas

We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…

Signal Processing · Electrical Eng. & Systems 2020-03-04 Dominik Reinhard , Michael Fauß , Abdelhak M. Zoubir

In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…

Information Theory · Computer Science 2025-01-07 Ching-Fang Li , I-Hsiang Wang

This paper studies the binary classification of two distributions with the same Gaussian copula in high dimensions. Under this semiparametric Gaussian copula setting, we derive an accurate semiparametric estimator of the log density ratio,…

Statistics Theory · Mathematics 2014-11-12 Yue Zhao , Marten Wegkamp