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We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…

Data Structures and Algorithms · Computer Science 2020-09-15 Ilias Diakonikolas , Themis Gouleakis , Daniel M. Kane , John Peebles , Eric Price

The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…

Data Structures and Algorithms · Computer Science 2022-09-22 Sourav Chakraborty , Eldar Fischer , Arijit Ghosh , Gopinath Mishra , Sayantan Sen

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

Machine Learning · Computer Science 2024-12-03 Maryam Aliakbarpour , Piotr Indyk , Ronitt Rubinfeld , Sandeep Silwal

Testing whether the observed data conforms to a purported model (probability distribution) is a basic and fundamental statistical task, and one that is by now well understood. However, the standard formulation, identity testing, fails to…

Statistics Theory · Mathematics 2021-05-06 Clément L. Canonne , Karl Wimmer

There has been considerable recent interest in distribution-tests whose run-time and sample requirements are sublinear in the domain-size $k$. We study two of the most important tests under the conditional-sampling model where each query…

Data Structures and Algorithms · Computer Science 2015-04-17 Moein Falahatgar , Ashkan Jafarpour , Alon Orlitsky , Venkatadheeraj Pichapathi , Ananda Theertha Suresh

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

A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability…

Data Structures and Algorithms · Computer Science 2014-09-16 Constantinos Daskalakis , Ilias Diakonikolas , Rocco A. Servedio

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 initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…

Machine Learning · Computer Science 2025-07-04 Ilias Diakonikolas , Jingyi Gao , Daniel Kane , Sihan Liu , Christopher Ye

In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$,…

Data Structures and Algorithms · Computer Science 2019-07-09 Maryam Aliakbarpour , Themis Gouleakis , John Peebles , Ronitt Rubinfeld , Anak Yodpinyanee

Uniformity testing is one of the most well-studied problems in property testing, with many known test statistics, including ones based on counting collisions, singletons, and the empirical TV distance. It is known that the optimal sample…

Machine Learning · Statistics 2022-06-23 Shivam Gupta , Eric Price

In this paper, we advocate a novel measure for the purpose of checking the quality of a cluster partition for a sample into several distinct classes, and thus, determine the unknown value for the true number of clusters prevailing the…

Applications · Statistics 2024-04-12 Soumita Modak

The univariate quantile-quantile (Q-Q) plot is a well-known graphical tool for examining whether two data sets are generated from the same distribution or not. It is also used to determine how well a specified probability distribution fits…

Statistics Theory · Mathematics 2014-07-07 Subhra Sankar Dhar , Biman Chakraborty , Probal Chaudhuri

What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…

Data Structures and Algorithms · Computer Science 2022-05-13 Omar Fawzi , Nicolas Flammarion , Aurélien Garivier , Aadil Oufkir

Nonparametric detection of existence of an anomalous structure over a network is investigated. Nodes corresponding to the anomalous structure (if one exists) receive samples generated by a distribution q, which is different from a…

Machine Learning · Statistics 2017-10-11 Shaofeng Zou , Yingbin Liang , H. Vincent Poor

A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…

Statistics Theory · Mathematics 2024-06-11 Antonio Di Noia , Marzia Marcheselli , Caterina Pisani , Luca Pratelli

We propose new goodness-of-fit tests for the Poisson distribution. The testing procedure entails fitting a weighted Poisson distribution, which has the Poisson as a special case, to observed data. Based on sample data, we calculate an…

Methodology · Statistics 2024-02-21 Winnie Kirui , Elzanie Bothma , Marius Smuts , Anke Steyn , Jaco Visagie

Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a…

Applications · Statistics 2020-12-07 Wolfgang Rolke

In this paper, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, the sample complexity of testing properties of joint distributions is exponential…

Computational Complexity · Computer Science 2022-08-03 Rishiraj Bhattacharyya , Sourav Chakraborty

Testing hypotheses of goodness-of-fit about mixture distributions on the basis of independent but not necessarily identically distributed random vectors is considered. The hypotheses are given by a specific distribution or by a family of…

Statistics Theory · Mathematics 2016-04-21 Daniel Gaigall