Related papers: Sharp Bounds for Generalized Uniformity Testing
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…
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…
The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…
Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected…
We consider the problem of testing whether an unknown unitary is close to a specified level of the Clifford hierarchy. Bu, Gu, and Jaffe proposed a candidate tester for this task based on a connection with noncommutative analogues of the…
We analyze the sample complexity of full-batch Gradient Descent (GD) in the setup of non-smooth Stochastic Convex Optimization. We show that the generalization error of GD, with common choice of hyper-parameters, can be $\tilde \Theta(d/m +…
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 $\varepsilon > 0$, $m_1$…
Results on the hardness of approximate sampling are seen as important stepping stones towards a convincing demonstration of the superior computational power of quantum devices. The most prominent suggestions for such experiments include…
We study a new framework for property testing of probability distributions, by considering distribution testing algorithms that have access to a conditional sampling oracle.* This is an oracle that takes as input a subset $S \subseteq [N]$…
A preferential domain is a collection of sets of preferences which are linear orders over a set of alternatives. These domains have been studied extensively in social choice theory due to both its practical importance and theoretical…
In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known covariance and product…
Sum-based global tests are highly popular in multiple hypothesis testing. In this paper we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDP),…
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…
We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…
When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different…
We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions. Given oracle access to an unknown Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$ and sampling oracle access to an unknown distribution…
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…
Given samples from an unknown distribution $p$ and a description of a distribution $q$, are $p$ and $q$ close or far? This question of "identity testing" has received significant attention in the case of testing whether $p$ and $q$ are…
A class of discrete probability distributions contains distributions with limited support, i.e. possible argument values are limited to a set of numbers (typically consecutive). Examples of such data are results from subjective experiments…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…