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Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…

Machine Learning · Statistics 2019-10-02 M. Scetbon , G. Varoquaux

We study the fundamental problems of (i) uniformity testing of a discrete distribution, and (ii) closeness testing between two discrete distributions with bounded $\ell_2$-norm. These problems have been extensively studied in distribution…

Data Structures and Algorithms · Computer Science 2016-11-14 Ilias Diakonikolas , Themis Gouleakis , John Peebles , Eric Price

Motivated by the fact that input distributions are often unknown in advance, distribution-free property testing considers a setting where the algorithmic task is to accept functions $f : [n] \to \{0,1\}$ with a certain property P and reject…

Computational Complexity · Computer Science 2024-02-19 Hugo Aaronson , Tom Gur , Ninad Rajgopal , Ron D. Rothblum

The Huge Object model is a distribution testing model in which we are given access to independent samples from an unknown distribution over the set of strings $\{0,1\}^n$, but are only allowed to query a few bits from the samples. We…

Data Structures and Algorithms · Computer Science 2024-09-18 Tomer Adar , Eldar Fischer , Amit Levi

This paper provides a new unimodality test with application in hierarchical clustering methods. The proposed method denoted by signature test (Sigtest), transforms the data based on its statistics. The transformed data has much smaller…

Machine Learning · Computer Science 2014-01-10 Mahdi Shahbaba , Soosan Beheshti

In this paper, we characterize compatibility of distributions and probability measures on a measurable space. For a set of indices $\mathcal J$, we say that the tuples of probability measures $(Q_i)_{i\in \mathcal J} $ and distributions…

Probability · Mathematics 2019-04-16 Jie Shen , Yi Shen , Bin Wang , Ruodu Wang

We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…

Data Structures and Algorithms · Computer Science 2025-06-05 Jan Seyfried , Sayantan Sen , Marco Tomamichel

Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…

Methodology · Statistics 2025-10-29 Luke Hagar , Nathaniel T. Stevens

Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular,…

Machine Learning · Statistics 2026-04-13 Rohan Hore , Rina Foygel Barber

In this article, a novel identification test is proposed, which can be applied to parameteric models such as Mixture of Normal (MN) distributions, Markow Switching(MS), or Structural Autoregressive (SVAR) models. In the approach, it is…

Methodology · Statistics 2022-06-09 Katarzyna Maciejowska

Continuous and strictly positive data that exhibit skewness and outliers frequently arise in many applied disciplines. Log-symmetric distributions provide a flexible framework for modeling such data. In this article, we develop new…

Methodology · Statistics 2026-02-16 Ganesh Vishnu Avhad , Sudheesh K. Kattumannil

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

Statistics Theory · Mathematics 2022-02-17 Jack Noonan , Anatoly Zhigljavsky

In this article, we propose a one-sample test to check whether the support of the unknown distribution generating the data is homologically equivalent to the support of some specified distribution or not OR using the corresponding…

Methodology · Statistics 2023-12-01 Satish Kumar , Subhra Sankar Dhar

For a distribution $p:=\{p_k\}_{k=1}^\infty$ on the positive integers, there are two natural ways to construct a random permutation in $S_n$ or of $\mathbb{N}$ from IID samples from $p$--the $p$-biased construction and the $p$-shifted…

Probability · Mathematics 2021-02-23 Ross G. Pinsky

The sample complexity of simple binary hypothesis testing is the smallest number of i.i.d.\ samples required to distinguish between two distributions $p$ and $q$ in either: (i) the prior-free setting, with type-I error at most $\alpha$ and…

Statistics Theory · Mathematics 2025-05-27 Ankit Pensia , Varun Jog , Po-Ling Loh

We consider goodness-of-fit tests with i.i.d. samples generated from a categorical distribution $(p_1,...,p_k)$. For a given $(q_1,...,q_k)$, we test the null hypothesis whether $p_j=q_{\pi(j)}$ for some label permutation $\pi$. The…

Statistics Theory · Mathematics 2018-07-30 Chao Gao

In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…

Statistics Theory · Mathematics 2024-04-22 Long-Hao Xu , Tobias Mütze , Frank Konietschke , Tim Friede

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

In this paper, we address the problem of testing goodness-of-fit for discrete distributions, where we focus on the geometric distribution. We define new likelihood-based goodness-of-fit tests using the beta-geometric distribution and the…

Statistics Theory · Mathematics 2020-10-09 Rasmus Erlemann , Bo Henry Lindqvist

Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…

Machine Learning · Computer Science 2013-05-03 Somayeh Danafar , Paola M. V. Rancoita , Tobias Glasmachers , Kevin Whittingstall , Juergen Schmidhuber