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Related papers: Optimal Testing for Properties of Distributions

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Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-12-04 Uri Meir

We consider the closeness testing problem for discrete distributions. The goal is to distinguish whether two samples are drawn from the same unspecified distribution, or whether their respective distributions are separated in $L_1$-norm. In…

Statistics Theory · Mathematics 2021-01-20 Joseph Lam-Weil , Alexandra Carpentier , Bharath K. Sriperumbudur

We consider the identity testing problem - or goodness-of-fit testing problem - in multivariate binomial families, multivariate Poisson families and multinomial distributions. Given a known distribution $p$ and $n$ iid samples drawn from an…

Statistics Theory · Mathematics 2022-04-26 J. Chhor , A. Carpentier

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…

Data Structures and Algorithms · Computer Science 2018-07-03 Clément L. Canonne , Ilias Diakonikolas , Daniel M. Kane , Alistair Stewart

We consider the problem of $L_p$-testing of class of bounded derivative properties over hypergrid domain with points distributed according to some product distribution. This class includes monotonicity, the Lipschitz property,…

Data Structures and Algorithms · Computer Science 2014-05-02 Kashyap Dixit

We consider the problem of learning a discrete distribution in the presence of an $\epsilon$ fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, $p$, and each data source…

Machine Learning · Computer Science 2017-11-23 Mingda Qiao , Gregory Valiant

The primary problem in property testing is to decide whether a given function satisfies a certain property, or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion…

Discrete Mathematics · Computer Science 2014-04-04 Deeparnab Chakrabarty , Kashyap Dixit , Madhav Jha , C. Seshadhri

We investigate distribution testing with access to non-adaptive conditional samples. In the conditional sampling model, the algorithm is given the following access to a distribution: it submits a query set $S$ to an oracle, which returns a…

Data Structures and Algorithms · Computer Science 2018-11-06 Gautam Kamath , Christos Tzamos

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…

Statistics Theory · Mathematics 2007-06-13 Peter Hall , Ingrid Van Keilegom

In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…

Data Structures and Algorithms · Computer Science 2025-08-05 Guy Blanc , Clément L. Canonne , Erik Waingarten

Sampling algorithms play a pivotal role in probabilistic AI. However, verifying if a sampler program indeed samples from the claimed distribution is a notoriously hard problem. Provably correct testers like Barbarik, Teq, Flash, CubeProbe…

Data Structures and Algorithms · Computer Science 2025-12-09 Rishiraj Bhattacharyya , Sourav Chakraborty , Yash Pote , Uddalok Sarkar , Sayantan Sen

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

We study the fundamental problem of estimating an unknown discrete distribution $p$ over $d$ symbols, given $n$ i.i.d. samples from the distribution. We are interested in minimizing the KL divergence between the true distribution and the…

Machine Learning · Statistics 2025-05-30 Jiayuan Ye , Vitaly Feldman , Kunal Talwar

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 study distribution-free property testing and learning problems where the unknown probability distribution is a product distribution over $\mathbb{R}^d$. For many important classes of functions, such as intersections of halfspaces,…

Data Structures and Algorithms · Computer Science 2021-11-17 Nathaniel Harms , Yuichi Yoshida

We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over $k$ elements, under differential privacy. While the problems have a long history in statistics, finite…

Machine Learning · Computer Science 2017-11-01 Jayadev Acharya , Ziteng Sun , Huanyu Zhang

Let $\mathfrak{C}$ be a class of probability distributions over the discrete domain $[n] = \{1,...,n\}.$ We show that if $\mathfrak{C}$ satisfies a rather general condition -- essentially, that each distribution in $\mathfrak{C}$ can be…

Machine Learning · Computer Science 2012-10-03 Siu-on Chan , Ilias Diakonikolas , Rocco A. Servedio , Xiaorui Sun

Private closeness testing asks to decide whether the underlying probability distributions of two sensitive datasets are identical or differ significantly in statistical distance, while guaranteeing (differential) privacy of the data. As in…

Data Structures and Algorithms · Computer Science 2023-09-14 Clément L. Canonne , Yucheng Sun

The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…

Methodology · Statistics 2020-01-01 Ayanendranath Basu , Abhijit Mandal , Nirian Martin , Leandro Pardo

In multiple classification, one aims to determine whether a testing sequence is generated from the same distribution as one of the M training sequences or not. Unlike most of existing studies that focus on discrete-valued sequences with…

Machine Learning · Statistics 2024-10-30 Lina Zhu , Lin Zhou