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A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…
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 study the problem of testing identity against a given distribution with a focus on the high confidence regime. More precisely, given samples from an unknown distribution $p$ over $n$ elements, an explicitly given distribution $q$, and…
We consider the problem of testing distribution identity. Given a sequence of independent samples from an unknown distribution on a domain of size n, the goal is to check if the unknown distribution approximately equals a known distribution…
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…
We study the problem of testing identity of a collection of unknown quantum states given sample access to this collection, each state appearing with some known probability. We show that for a collection of $d$-dimensional quantum states of…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
We study the impact of quantum computation on the fundamental problem of testing the property of distributions. In particular, we focus on testing whether two unknown classical distributions are close or far enough, and propose the…
In this paper, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, the sample complexity of testing properties of joint distributions is exponential…
We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution…
Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…
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…
The classical coding theorem in Kolmogorov complexity states that if an $n$-bit string $x$ is sampled with probability $\delta$ by an algorithm with prefix-free domain then K$(x) \leq \log(1/\delta) + O(1)$. In a recent work, Lu and…
We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over $k$ elements, under differential privacy. While the problems have a long history in statistics, finite…
We investigate the problem of identity testing for multidimensional histogram distributions. A distribution $p: D \rightarrow \mathbb{R}_+$, where $D \subseteq \mathbb{R}^d$, is called a $k$-histogram if there exists a partition of the…
Sampling algorithms play a pivotal role in probabilistic AI. However, verifying if a sampler program indeed samples from the claimed distribution is a notoriously hard problem. Provably correct testers like Barbarik, Teq, Flash, CubeProbe…
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…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…