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We express the joint R\'enyi entropy of progressively censored order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint R\'enyi entropy of progressively Type-II censored data.…

Methodology · Statistics 2013-03-25 Akram Kohansal , Saeid Rezakhah

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…

Information Theory · Computer Science 2018-04-06 Ramji Venkataramanan , Oliver Johnson

We revisit the problem of asymmetric binary hypothesis testing against a composite alternative hypothesis. We introduce a general framework to treat such problems when the alternative hypothesis adheres to certain axioms. In this case we…

Information Theory · Computer Science 2017-12-12 Marco Tomamichel , Masahito Hayashi

For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$,…

Probability · Mathematics 2024-06-21 Sergey G. Bobkov , Friedrich Götze

In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…

Methodology · Statistics 2022-08-03 Tianyu Zhan , Jian Kang

Hypothesis exclusion is an information-theoretic task in which an experimenter aims at ruling out a false hypothesis from a finite set of known candidates, and an error occurs if and only if the hypothesis being ruled out is the ground…

Quantum Physics · Physics 2026-05-28 Kaiyuan Ji , Hemant K. Mishra , Milán Mosonyi , Mark M. Wilde

Uniform sampling over a convex body is a fundamental algorithmic problem, yet the convergence in KL or R\'enyi divergence of most samplers remains poorly understood. In this work, we propose a constrained proximal sampler, a principled and…

Data Structures and Algorithms · Computer Science 2024-07-19 Yunbum Kook , Matthew S. Zhang

We show finite-size bounds on the deviation of the optimal type II error from its asymptotic value in the quantum hypothesis testing problem of Stein's lemma with composite null-hypothesis. The proof is based on some simple properties of a…

Quantum Physics · Physics 2014-07-07 Milán Mosonyi

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

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

Information Theory · Computer Science 2018-12-07 Lin Zhou , Vincent Y. F. Tan , Mehul Motani

This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction…

Information Theory · Computer Science 2025-06-18 Hadi Kazemi , Ankit Pensia , Varun Jog

The random variable simulation problem consists in using a $k$-dimensional i.i.d. random vector $X^{k}$ with distribution $P_{X}^{k}$ to simulate an $n$-dimensional i.i.d. random vector $Y^{n}$ so that its distribution is approximately…

Information Theory · Computer Science 2018-12-24 Lei Yu , Vincent Y. F. Tan

This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…

Statistics Theory · Mathematics 2021-11-29 Sebastian Espinosa , Jorge F. Silva , Pablo Piantanida

In supervised learning, we often face with ambiguous (A) samples that are difficult to label even by domain experts. In this paper, we consider a binary classification problem in the presence of such A samples. This problem is substantially…

Machine Learning · Computer Science 2020-11-25 Naoya Otani , Yosuke Otsubo , Tetsuya Koike , Masashi Sugiyama

Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…

Statistics Theory · Mathematics 2024-04-09 Remo Kretschmann , Daniel Wachsmuth , Frank Werner

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the…

Information Theory · Computer Science 2016-04-07 Gonzalo Vazquez-Vilar , Adrià Tauste Campo , Albert Guillén i Fàbregas , Alfonso Martinez

When testing for replication of results from a primary study with two-sided hypotheses in a follow-up study, we are usually interested in discovering the features with discoveries in the same direction in the two studies. The direction of…

Methodology · Statistics 2015-03-10 Ruth Heller , Marina Bogomolov , Yoav Benjamini , Tamar Sofer

Previous results on certain sampling series have left open if divergence only occurs for certain subsequences or, in fact, in the limit. Here we prove that divergence occurs in the limit. We consider three canonical reconstruction methods…

Information Theory · Computer Science 2014-04-18 Holger Boche , Brendan Farrell

After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…

Methodology · Statistics 2020-07-07 Oliver Dukes , Vahe Avagyan , Stijn Vansteelandt

A number of biomedical problems require performing many hypothesis tests, with an attendant need to apply stringent thresholds. Often the data take the form of a series of predictor vectors, each of which must be compared with a single…

Methodology · Statistics 2014-05-13 Yi-Hui Zhou , Fred Wright