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Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as…

Data Structures and Algorithms · Computer Science 2025-10-23 Maryam Aliakbarpour , Zhan Shi , Ria Stevens , Vincent X. Wang

Alice and Bob want to know if two strings of length n are almost equal. That is, do they differ on \textit{at most} a bits? Let 0\leq a\leq n-1. We show that any deterministic protocol, as well as any error-free quantum protocol (C*…

Computational Complexity · Computer Science 2015-01-13 Andris Ambainis , William Gasarch , Aravind Srinavasan , Andrey Utis

We consider an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. two histograms are drawn from the same distribution). The…

Data Analysis, Statistics and Probability · Physics 2013-11-26 S. Bityukov , N. Krasnikov , A. Nikitenko , V. Smirnova

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

Data Structures and Algorithms · Computer Science 2023-10-25 Andre Linhares , Chaitanya Swamy

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Statistics Theory · Mathematics 2022-11-15 Loris Michel , Jeffrey Näf , Nicolai Meinshausen

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

Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…

Discrete Mathematics · Computer Science 2024-11-15 Yiqiao Bao , Sampath Kannan , Erik Waingarten

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

Although many authors have considered how many ternary comparisons it takes to sort a multiset $S$ of size $n$, the best known upper and lower bounds still differ by a term linear in $n$. In this paper we restrict our attention to online…

Data Structures and Algorithms · Computer Science 2009-07-07 Travis Gagie , Yakov Nekrich

In recent years, neural networks have demonstrated their remarkable ability to discern intricate patterns and relationships from raw data. However, understanding the inner workings of these black box models remains challenging, yet crucial…

Machine Learning · Statistics 2024-04-18 Niklas Koenen , Marvin N. Wright

Adaptivity is an important feature of data analysis---typically the choice of questions asked about a dataset depends on previous interactions with the same dataset. However, generalization error is typically bounded in a non-adaptive…

Machine Learning · Computer Science 2015-11-11 Raef Bassily , Adam Smith , Thomas Steinke , Jonathan Ullman

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

Whilst an abundance of techniques have recently been proposed to generate counterfactual explanations for the predictions of opaque black-box systems, markedly less attention has been paid to exploring the uncertainty of these generated…

Machine Learning · Computer Science 2021-07-22 Eoin Delaney , Derek Greene , Mark T. Keane

The task of the binary classification problem is to determine which of two distributions has generated a length-$n$ test sequence. The two distributions are unknown; two training sequences of length $N$, one from each distribution, are…

Information Theory · Computer Science 2016-04-18 Dayu Huang , Sean Meyn

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 review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…

Methodology · Statistics 2024-11-19 Edgar C. Merkle , Oludare Ariyo , Sonja D. Winter , Mauricio Garnier-Villarreal

We study the problem of testing identity against a given distribution with a focus on the high confidence regime. More precisely, given samples from an unknown distribution $p$ over $n$ elements, an explicitly given distribution $q$, and…

Data Structures and Algorithms · Computer Science 2019-01-17 Ilias Diakonikolas , Themis Gouleakis , John Peebles , Eric Price

Anomaly detection is not an easy problem since distribution of anomalous samples is unknown a priori. We explore a novel method that gives a trade-off possibility between one-class and two-class approaches, and leads to a better performance…

Machine Learning · Statistics 2020-05-26 Maxim Borisyak , Artem Ryzhikov , Andrey Ustyuzhanin , Denis Derkach , Fedor Ratnikov , Olga Mineeva

We are interested in testing properties of distributions with systematically mislabeled samples. Our goal is to make decisions about unknown probability distributions, using a sample that has been collected by a confused collector, such as…

Data Structures and Algorithms · Computer Science 2023-11-27 Renato Ferreira Pinto , Nathaniel Harms

A great deal of inference in statistics is based on making the approximation that a statistic is normally distributed. The error in doing so is generally $O(n^{-1/2})$ and can be very considerable when the distribution is heavily biased or…

Methodology · Statistics 2010-09-14 C. S. Withers , S. Nadarajah