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We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…

Data Structures and Algorithms · Computer Science 2025-11-05 Shivam Garg , Chirag Pabbaraju , Kirankumar Shiragur , Gregory Valiant

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 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

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

We investigate the problem of testing whether a discrete probability distribution over an ordered domain is a histogram on a specified number of bins. One of the most common tools for the succinct approximation of data, $k$-histograms over…

Data Structures and Algorithms · Computer Science 2022-07-15 Clément L. Canonne , Ilias Diakonikolas , Daniel M. Kane , Sihan Liu

We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit…

Information Theory · Computer Science 2010-08-24 Yuriy A. Reznik

We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…

Data Structures and Algorithms · Computer Science 2019-07-23 Jayadev Acharya , Clément L. Canonne , Yanjun Han , Ziteng Sun , Himanshu Tyagi

We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution…

Data Structures and Algorithms · Computer Science 2022-07-26 Shyam Narayanan

We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…

Data Structures and Algorithms · Computer Science 2025-12-10 Gunjan Kumar , Yash Pote , Jonathan Scarlett

In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…

Information Theory · Computer Science 2022-06-22 Tomer Berg , Or Ordentlich , Ofer Shayevitz

We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…

Quantum Physics · Physics 2024-11-08 Clément L. Canonne , Robin Kothari , Ryan O'Donnell

A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…

Data Structures and Algorithms · Computer Science 2014-10-15 Jayadev Acharya , Constantinos Daskalakis

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

The field of property testing of probability distributions, or distribution testing, aims to provide fast and (most likely) correct answers to questions pertaining to specific aspects of very large datasets. In this work, we consider a…

Data Structures and Algorithms · Computer Science 2015-04-27 Clément L. Canonne

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

Recently, there has been significant work studying distribution testing under the Conditional Sampling model. In this model, a query specifies a subset $S$ of the domain, and the output received is a sample drawn from the distribution…

Data Structures and Algorithms · Computer Science 2020-11-05 Shyam Narayanan

We study robust testing and estimation of discrete distributions in the strong contamination model. We consider both the "centralized setting" and the "distributed setting with information constraints" including communication and local…

Information Theory · Computer Science 2021-04-23 Jayadev Acharya , Ziteng Sun , Huanyu Zhang

One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When…

Quantum Physics · Physics 2026-05-15 Bruno Cavalar , Eli Goldin , Matthew Gray , Taiga Hiroka , Min-Hsiu Hsieh , Tomoyuki Morimae

We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1,1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)).…

Data Structures and Algorithms · Computer Science 2021-02-08 Clément L. Canonne , Xi Chen , Gautam Kamath , Amit Levi , Erik Waingarten

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