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We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…

Machine Learning · Computer Science 2018-07-10 Alkis Gotovos , Hamed Hassani , Andreas Krause , Stefanie Jegelka

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

Consider a sequence (indexed by n) of Markov chains Z^n in R^d characterized by transition kernels that approximately (in n) depend only on the rescaled state n^{-1} Z^n. Subject to a smoothness condition, such a family can be closely…

Probability · Mathematics 2009-08-17 Kamil Szczegot

The objective of goodness-of-fit testing is to assess whether a dataset of observations is likely to have been drawn from a candidate probability distribution. This paper presents a rank-based family of goodness-of-fit tests that is…

Statistics Theory · Mathematics 2019-04-18 Feras A. Saad , Cameron E. Freer , Nathanael L. Ackerman , Vikash K. Mansinghka

Hypothesis Selection is a fundamental distribution learning problem where given a comparator-class $Q=\{q_1,\ldots, q_n\}$ of distributions, and a sampling access to an unknown target distribution $p$, the goal is to output a distribution…

Machine Learning · Computer Science 2021-08-19 Olivier Bousquet , Mark Braverman , Klim Efremenko , Gillat Kol , Shay Moran

Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…

Optimization and Control · Mathematics 2025-09-30 Srećko Đurašinović , Jean-Bernard Lasserre , Victor Magron

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…

Methodology · Statistics 2016-11-30 Xu Chen , Shaan Qamar , Surya T. Tokdar

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…

Data Structures and Algorithms · Computer Science 2015-06-03 Jayadev Acharya , Ilias Diakonikolas , Jerry Li , Ludwig Schmidt

We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…

Information Theory · Computer Science 2011-07-25 Chun Lam Chan , Pak Hou Che , Sidharth Jaggi , Venkatesh Saligrama

The study of networks leads to a wide range of high dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in…

This paper considers the problem of testing many moment inequalities, where the number of moment inequalities ($p$) is possibly larger than the sample size ($n$). Chernozhukov et al. (2019) proposed asymptotic tests for this problem using…

Statistics Theory · Mathematics 2020-06-09 Nick Koning , Paul Bekker

In this paper, we study the problem of determining $k$ anomalous random variables that have different probability distributions from the rest $(n-k)$ random variables. Instead of sampling each individual random variable separately as in the…

Information Theory · Computer Science 2024-09-09 Myung Cho , Weiyu Xu , Lifeng Lai

Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of…

Quantum Physics · Physics 2025-11-12 Xiaoyu Liu , Jordi Tura , Albert Rico

We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target in total…

Machine Learning · Computer Science 2018-06-05 Hassan Ashtiani , Shai Ben-David , Abbas Mehrabian

A striking result of [Acharya et al. 2017] showed that to estimate symmetric properties of discrete distributions, plugging in the distribution that maximizes the likelihood of observed multiset of frequencies, also known as the profile…

Statistics Theory · Mathematics 2020-11-03 Yanjun Han , Kirankumar Shiragur

We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform…

Data Structures and Algorithms · Computer Science 2021-01-21 Jayadev Acharya , Clément L. Canonne , Cody Freitag , Ziteng Sun , Himanshu Tyagi

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…

Information Theory · Computer Science 2022-07-07 Minh Thanh Vu

We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…

Cryptography and Security · Computer Science 2022-06-03 Priyanka Golia , Brendan Juba , Kuldeep S. Meel

The distribution closeness testing (DCT) assesses whether the distance between a distribution pair is at least $\epsilon$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete one-dimensional…

Machine Learning · Computer Science 2025-10-10 Zhijian Zhou , Liuhua Peng , Xunye Tian , Feng Liu

We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…

Methodology · Statistics 2026-01-14 Alberto Bordino , Thomas B. Berrett