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Related papers: $\ell_p$ Testing and Learning of Discrete Distribu…

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We study the fundamental problem of estimating an unknown discrete distribution $p$ over $d$ symbols, given $n$ i.i.d. samples from the distribution. We are interested in minimizing the KL divergence between the true distribution and the…

Machine Learning · Statistics 2025-05-30 Jiayuan Ye , Vitaly Feldman , Kunal Talwar

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…

Machine Learning · Computer Science 2025-07-04 Ilias Diakonikolas , Jingyi Gao , Daniel Kane , Sihan Liu , Christopher Ye

Consider the communication-constrained estimation of discrete distributions under $\ell^p$ losses, where each distributed terminal holds multiple independent samples and uses limited number of bits to describe the samples. We obtain the…

Machine Learning · Computer Science 2024-11-11 Deheng Yuan , Tao Guo , Zhongyi Huang

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

Numerical Analysis · Mathematics 2020-08-05 Ken'ichiro Tanaka , Alexis Akira Toda

We give highly efficient algorithms, and almost matching lower bounds, for a range of basic statistical problems that involve testing and estimating the L_1 distance between two k-modal distributions $p$ and $q$ over the discrete domain…

Data Structures and Algorithms · Computer Science 2011-12-26 Constantinos Daskalakis , Ilias Diakonikolas , Rocco A. Servedio , Gregory Valiant , Paul Valiant

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 consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$,…

Data Structures and Algorithms · Computer Science 2019-07-09 Maryam Aliakbarpour , Themis Gouleakis , John Peebles , Ronitt Rubinfeld , Anak Yodpinyanee

Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust…

Machine Learning · Computer Science 2024-04-04 Nika Haghtalab , Michael I. Jordan , Eric Zhao

We give a formal verification procedure that decides whether a classifier ensemble is robust against arbitrary randomized attacks. Such attacks consist of a set of deterministic attacks and a distribution over this set. The…

Machine Learning · Computer Science 2020-07-10 Dennis Gross , Nils Jansen , Guillermo A. Pérez , Stephan Raaijmakers

We investigate distribution testing with access to non-adaptive conditional samples. In the conditional sampling model, the algorithm is given the following access to a distribution: it submits a query set $S$ to an oracle, which returns a…

Data Structures and Algorithms · Computer Science 2018-11-06 Gautam Kamath , Christos Tzamos

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

Statistics Theory · Mathematics 2022-02-17 Bhaswar B. Bhattacharya , Rajarshi Mukherjee

We consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the…

Statistics Theory · Mathematics 2018-10-18 Min Ye , Alexander Barg

The Huge Object model is a distribution testing model in which we are given access to independent samples from an unknown distribution over the set of strings $\{0,1\}^n$, but are only allowed to query a few bits from the samples. We…

Data Structures and Algorithms · Computer Science 2024-09-18 Tomer Adar , Eldar Fischer , Amit Levi

Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…

Probability · Mathematics 2012-09-21 Marco Ferrante , Nadia Frigo

We consider the problem of estimating the $L_1$ distance between two discrete probability measures $P$ and $Q$ from empirical data in a nonasymptotic and large alphabet setting. When $Q$ is known and one obtains $n$ samples from $P$, we…

Statistics Theory · Mathematics 2018-06-26 Jiantao Jiao , Yanjun Han , Tsachy Weissman

Oblivious low-distortion subspace embeddings are a crucial building block for numerical linear algebra problems. We show for any real $p, 1 \leq p < \infty$, given a matrix $M \in \mathbb{R}^{n \times d}$ with $n \gg d$, with constant…

Data Structures and Algorithms · Computer Science 2014-03-19 David P. Woodruff , Qin Zhang

Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation…

Machine Learning · Computer Science 2023-11-22 Swati Padmanabhan , David P. Woodruff , Qiuyi Zhang

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Statistics Theory · Mathematics 2023-09-06 Youssef Marzouk , Zhi Ren , Sven Wang , Jakob Zech

We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…

Data Analysis, Statistics and Probability · Physics 2018-12-26 Igor Volobouev , A. Alexandre Trindade

Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…

Information Theory · Computer Science 2007-07-13 Thomas Holenstein , Renato Renner
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