Related papers: Testing Shape Restrictions of Discrete Distributio…
In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…
Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically…
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…
Given samples from two distributions over an $n$-element set, we wish to test whether these distributions are statistically close. We present an algorithm which uses sublinear in $n$, specifically, $O(n^{2/3}\epsilon^{-8/3}\log n)$,…
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…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing,…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
In recent studies, the generalization properties for distributed learning and random features assumed the existence of the target concept over the hypothesis space. However, this strict condition is not applicable to the more common…
We consider the problem of determining which classes of functions can be tested more efficiently than they can be learned, in the distribution-free sample-based model that corresponds to the standard PAC learning setting. Our main result…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
This paper studies the problem of {\em learning} the probability distribution $P_X$ of a discrete random variable $X$ using indirect and sequential samples. At each time step, we choose one of the possible $K$ functions, $g_1, \ldots, g_K$…
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…
A variety of statistics based on sample spacings has been studied in the literature for testing goodness-of-fit to parametric distributions. To test the goodness-of-fit to a nonparametric class of univariate shape-constrained densities,…
Given samples from an unknown multivariate distribution $p$, is it possible to distinguish whether $p$ is the product of its marginals versus $p$ being far from every product distribution? Similarly, is it possible to distinguish whether…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…
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…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…