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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…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
In this note, we revisit the recent work of Diakonikolas, Gouleakis, Kane, Peebles, and Price (2021), and provide an alternative proof of their main result. Our argument does not rely on any specific property of Poisson random variables…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…
We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…
This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the…
Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…
We propose and axiomatize preferences on a product state space in light of uncertainty regarding the dependency of different payoff-relevant factors. Dependence structures allow to decompose probabilities and allow to pin down behavior…
Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing…
In many fairness and distribution robustness problems, one has access to labeled data from multiple source distributions yet the test data may come from an arbitrary member or a mixture of them. We study the problem of constructing a…
Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the…
We consider the problem of testing independence in mixed-type data that combine count variables with positive, absolutely continuous variables. We first introduce two distinct classes of test statistics in the bivariate setting, designed to…
The classic problems of testing uniformity of and learning a discrete distribution, given access to independent samples from it, are examined under general $\ell_p$ metrics. The intuitions and results often contrast with the classic…