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Uniformity testing is one of the most well-studied problems in property testing, with many known test statistics, including ones based on counting collisions, singletons, and the empirical TV distance. It is known that the optimal sample…

Machine Learning · Statistics 2022-06-23 Shivam Gupta , Eric Price

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…

Data Structures and Algorithms · Computer Science 2022-03-07 Clément L. Canonne , Gautam Kamath , Audra McMillan , Jonathan Ullman , Lydia Zakynthinou

The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…

Computational Complexity · Computer Science 2016-08-31 Peter Gacs

As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify…

Computational Complexity · Computer Science 2024-09-11 Tal Herman , Guy Rothblum

We present an empirical analysis of data structures for approximate nearest neighbor searching. We compare the well-known optimized kd-tree splitting method against two alternative splitting methods. The first, called the sliding-midpoint…

Computational Geometry · Computer Science 2007-05-23 Songrit Maneewongvatana , David M. Mount

We establish optimal Statistical Query (SQ) lower bounds for robustly learning certain families of discrete high-dimensional distributions. In particular, we show that no efficient SQ algorithm with access to an $\epsilon$-corrupted binary…

Data Structures and Algorithms · Computer Science 2022-06-10 Ilias Diakonikolas , Daniel M. Kane , Yuxin Sun

The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…

Data Structures and Algorithms · Computer Science 2021-01-21 Federico Altieri , Andrea Pietracaprina , Geppino Pucci , Fabio Vandin

Consider a finite set of sources, each producing i.i.d. observations that follow a unique probability distribution on a finite alphabet. We study the problem of matching a finite set of observed sequences to the set of sources under the…

Information Theory · Computer Science 2014-12-09 Jayakrishnan Unnikrishnan

In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…

Data Structures and Algorithms · Computer Science 2025-08-05 Guy Blanc , Clément L. Canonne , Erik Waingarten

We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1,1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)).…

Data Structures and Algorithms · Computer Science 2021-02-08 Clément L. Canonne , Xi Chen , Gautam Kamath , Amit Levi , Erik Waingarten

Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…

Machine Learning · Statistics 2020-09-04 Aditya Kela , Kai von Prillwitz , Johan Aberg , Rafael Chaves , David Gross

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…

Data Structures and Algorithms · Computer Science 2025-12-09 Rishiraj Bhattacharyya , Sourav Chakraborty , Yash Pote , Uddalok Sarkar , Sayantan Sen

Let $\theta_0,\theta_1 \in \mathbb{R}^d$ be the population risk minimizers associated to some loss $\ell:\mathbb{R}^d\times \mathcal{Z}\to\mathbb{R}$ and two distributions $\mathbb{P}_0,\mathbb{P}_1$ on $\mathcal{Z}$. The models…

Statistics Theory · Mathematics 2021-07-13 Dmitrii M. Ostrovskii , Mohamed Ndaoud , Adel Javanmard , Meisam Razaviyayn

We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…

Data Structures and Algorithms · Computer Science 2019-07-23 Jayadev Acharya , Clément L. Canonne , Yanjun Han , Ziteng Sun , Himanshu Tyagi

A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently…

Statistics Theory · Mathematics 2015-02-25 Emilie Kaufmann , Olivier Cappé , Aurélien Garivier

We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…

Machine Learning · Computer Science 2020-03-18 Yi Hao , Alon Orlitsky

We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…

Quantum Physics · Physics 2010-05-13 Sourav Chakraborty , Eldar Fischer , Arie Matsliah , Ronald de Wolf

Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p in P or from a distribution q in Q and wants to decide from which set the…

Information Theory · Computer Science 2020-07-20 Fernando G. S. L. Brandao , Aram W. Harrow , James R. Lee , Yuval Peres

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…

Data Structures and Algorithms · Computer Science 2017-11-01 Constantinos Daskalakis , Gautam Kamath , John Wright

K-Nearest Neighbours (k-NN) is a popular classification and regression algorithm, yet one of its main limitations is the difficulty in choosing the number of neighbours. We present a Bayesian algorithm to compute the posterior probability…

Machine Learning · Computer Science 2017-06-05 Giuseppe Nuti