Related papers: Likelihood-free hypothesis testing
Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of…
Consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternative hypothesis $Q$, and only $P$…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
We propose a universal classifier for binary Neyman-Pearson classification where null distribution is known while only a training sequence is available for the alternative distribution. The proposed classifier interpolates between…
We study finite-sample inference for the trade-off function of two unknown probability distributions, the function that traces the optimal type I/type II error frontier in binary testing. Given samples from distributions $P$ and $Q$, we…
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 $\varepsilon > 0$, $m_1$…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…
Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular,…
Hypothesis testing plays a central role in statistical inference, and is used in many settings where privacy concerns are paramount. This work answers a basic question about privately testing simple hypotheses: given two distributions $P$…
We investigate the statistical task of closeness (or equivalence) testing for multidimensional distributions. Specifically, given sample access to two unknown distributions $\mathbf p, \mathbf q$ on $\mathbb R^d$, we want to distinguish…
We consider a novel multivariate nonparametric two-sample testing problem where, under the alternative, distributions $P$ and $Q$ are separated in an integral probability metric over functions of bounded total variation (TV IPM). We propose…
The sample complexity of simple binary hypothesis testing is the smallest number of i.i.d.\ samples required to distinguish between two distributions $p$ and $q$ in either: (i) the prior-free setting, with type-I error at most $\alpha$ and…
A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two…
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…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
We consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternate hypothesis $Q$, and only $P$…
A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to $n$ independent and identically distributed samples, denoted by…
Binary hypothesis testing under the Neyman-Pearson formalism is a statistical inference framework for distinguishing data generated by two different source distributions. Privacy restrictions may require the curator of the data or the data…
In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…