Related papers: Local minimax rates for closeness testing of discr…
We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…
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…
We consider the problem of estimating the mean of a distribution supported by the $k$-dimensional probability simplex in the setting where an $\varepsilon$ fraction of observations are subject to adversarial corruption. A simple particular…
We consider testing the goodness-of-fit of a distribution against alternatives separated in sup norm. We study the twin settings of Poisson-generated count data with a large number of categories and high-dimensional multinomials. In…
We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$…
This paper tackles a fundamental inference problem: given $n$ observations from a distribution $P$ over $\mathbb{R}^d$ with unknown mean $\boldsymbol{\mu}$, we must form a confidence set for the index (or indices) corresponding to the…
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…
We investigate the problems of identity and closeness testing over a discrete population from random samples. Our goal is to develop efficient testers while guaranteeing Differential Privacy to the individuals of the population. We describe…
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…
We study the problem of sampling from a distribution under local differential privacy (LDP). Given a private distribution $P \in \mathcal{P}$, the goal is to generate a single sample from a distribution that remains close to $P$ in…
In this work, we study local minimax convergence estimation rates subject to $\epsilon$-differential privacy. Unlike worst-case rates, which may be conservative, algorithms that are locally minimax optimal must adapt to easy instances of…
Finding anonymization mechanisms to protect personal data is at the heart of recent machine learning research. Here, we consider the consequences of local differential privacy constraints on goodness-of-fit testing, i.e. the statistical…
We study the question of closeness testing for two discrete distributions. More precisely, given samples from two distributions $p$ and $q$ over an $n$-element set, we wish to distinguish whether $p=q$ versus $p$ is at least $\eps$-far from…
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…
We consider the problem of two-sample testing under a local differential privacy constraint where a permutation procedure is used to calibrate the tests. We develop testing procedures which are optimal up to logarithmic factors, for general…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
We find separation rates for testing multinomial or more general discrete distributions under the constraint of local differential privacy. We construct efficient randomized algorithms and test procedures, in both the case where only…
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…
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…
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…