Related papers: Likelihood-free hypothesis testing
We introduce a game-theoretic framework to study the hypothesis testing problem, in the presence of an adversary aiming at preventing a correct decision. Specifically, the paper considers a scenario in which an analyst has to decide whether…
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…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
We revisit the problem of tolerant distribution testing. That is, given samples from an unknown distribution $p$ over $\{1, \dots, n\}$, is it $\varepsilon_1$-close to or $\varepsilon_2$-far from a reference distribution $q$ (in total…
We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
Finite mixtures of multivariate normal distributions have been widely used in empirical applications in diverse fields such as statistical genetics and statistical finance. Testing the number of components in multivariate normal mixture…
We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting…
We study a variation of Bayesian M-ary hypothesis testing in which the test outputs a list of L candidates out of the M possible upon processing the observation. We study the minimum error probability of list hypothesis testing, where an…
We study the following independence testing problem: given access to samples from a distribution $P$ over $\{0,1\}^n$, decide whether $P$ is a product distribution or whether it is $\varepsilon$-far in total variation distance from any…
In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the…
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…
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…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
Pearson's chi-squared test, from 1900, is the standard statistical tool for "hypothesis testing on distributions": namely, given samples from an unknown distribution $Q$ that may or may not equal a hypothesis distribution $P$, we want to…
We study the question of identity testing for structured distributions. More precisely, given samples from a {\em structured} distribution $q$ over $[n]$ and an explicit distribution $p$ over $[n]$, we wish to distinguish whether $q=p$…
We consider the problem of Neyman-Pearson classification which models unbalanced classification settings where error w.r.t. a distribution $\mu_1$ is to be minimized subject to low error w.r.t. a different distribution $\mu_0$. Given a…
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…