English
Related papers

Related papers: Testing Poisson Binomial Distributions

200 papers

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

Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has…

Data Structures and Algorithms · Computer Science 2015-12-09 Jayadev Acharya , Constantinos Daskalakis , Gautam Kamath

We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…

Data Structures and Algorithms · Computer Science 2015-08-25 Ilias Diakonikolas , Daniel M. Kane , Vladimir Nikishkin

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 investigate the problem of testing the equivalence between two discrete histograms. A {\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been…

Data Structures and Algorithms · Computer Science 2017-03-07 Ilias Diakonikolas , Daniel M. Kane , Vladimir Nikishkin

We generalise the known fact that for binomial $X_{n,k} \sim \mathrm{Bin}(n, k/n)$ one has $\inf_{k>1,n} \mathrm{P}(X_{n,k} \geq k) \geq \lim_{k \to 1+}\mathrm{P}(X_{2,k} \geq k) = 1/4$ to cover probabilities of exceeding a constant shift…

Probability · Mathematics 2023-08-11 Tilo Wiklund

We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a…

Data Structures and Algorithms · Computer Science 2025-09-23 Hadley Black , Christopher Ye

We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…

Data Structures and Algorithms · Computer Science 2019-11-19 Maryam Aliakbarpour , Sandeep Silwal

This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution $P$ over $\{0,1\}^n$, given sample access to $P$. We show that the sample complexity of the problem is…

Machine Learning · Computer Science 2023-04-17 Vipul Arora , Arnab Bhattacharyya , Clément L. Canonne , Joy Qiping Yang

Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…

Probability · Mathematics 2009-03-26 K. M. Briggs , L. Song , T. Prellberg

Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…

Machine Learning · Statistics 2026-03-06 Maryam Aliakbarpour , Alireza Azizi , Ria Stevens

There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example,…

Statistics Theory · Mathematics 2019-07-09 Maryam Aliakbarpour , Ravi Kumar , Ronitt Rubinfeld

We study the problems of identity and closeness testing of $n$-dimensional product distributions. Prior works by Canonne, Diakonikolas, Kane and Stewart (COLT 2017) and Daskalakis and Pan (COLT 2017) have established tight sample complexity…

Data Structures and Algorithms · Computer Science 2021-05-27 Arnab Bhattacharyya , Sutanu Gayen , Saravanan Kandasamy , N. V. Vinodchandran

The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…

Methodology · Statistics 2022-09-14 Denis Talbot , Miceline Mésidor , Yohann Chiu , Marc Simard , Caroline Sirois

We introduce the problem of Poisson sampling over joins: compute a sample of the result of a join query by conceptually performing a Bernoulli trial for each join tuple, using a non-uniform and tuple-specific probability. We propose an…

Databases · Computer Science 2026-03-17 Liese Bekkers , Frank Neven , Lorrens Pantelis , Stijn Vansummeren

In this paper, we have developed a new class of sampling schemes for estimating parameters of binomial and Poisson distributions. Without any information of the unknown parameters, our sampling schemes rigorously guarantee prescribed levels…

Statistics Theory · Mathematics 2009-10-11 Xinjia Chen

In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…

Data Structures and Algorithms · Computer Science 2017-08-17 Tuğkan Batu , Clément L. Canonne

Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…

Statistics Theory · Mathematics 2020-11-10 Dmitriy Kunisky

We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the…

Probability · Mathematics 2026-03-11 Mark Broadie , Ina Petkova

We give a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by product, we obtain a simple proof of an interesting…

Statistics Theory · Mathematics 2014-08-19 P. Vellaisamy