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Related papers: On Practical Algorithms for Entropy Estimation and…

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Entropy is a fundamental property of a repertoire. Here, we present an efficient algorithm to estimate the entropy of types with the help of Zhang's estimator. The algorithm takes advantage of the fact that the number of different…

Computation and Language · Computer Science 2017-07-27 Antoni Lozano , Bernardino Casas , Chris Bentz , Ramon Ferrer-i-Cancho

For any real number $p > 0$, we nearly completely characterize the space complexity of estimating $\|A\|_p^p = \sum_{i=1}^n \sigma_i^p$ for $n \times n$ matrices $A$ in which each row and each column has $O(1)$ non-zero entries and whose…

Data Structures and Algorithms · Computer Science 2017-03-21 Yi Li , David P. Woodruff

We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…

Data Structures and Algorithms · Computer Science 2026-05-25 Clément L. Canonne , Yash Pote , Jonathan Scarlett , Joy Qiping Yang

We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning. Contrary to state-of-the-art streaming frequency estimation algorithms, which heavily rely on random…

Data Structures and Algorithms · Computer Science 2022-07-19 Dimitris Bertsimas , Vassilis Digalakis

An efficient approach to the calculation of the $\epsilon$-entropy is proposed. The method is based on the idea of looking at the information content of a string of data, by analyzing the signal only at the instants when the fluctuations…

chao-dyn · Physics 2009-10-31 M. Abel , L. Biferale , M. Cencini , M. Falcioni , D. Vergni , A. Vulpiani

Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…

Information Theory · Computer Science 2024-11-06 Bill Kay , Audun Myers , Thad Boydston , Emily Ellwein , Cameron Mackenzie , Iliana Alvarez , Erik Lentz

Frequency estimation is one of the most fundamental problems in streaming algorithms. Given a stream $S$ of elements from some universe $U=\{1 \ldots n\}$, the goal is to compute, in a single pass, a short sketch of $S$ so that for any…

Data Structures and Algorithms · Computer Science 2021-11-09 Piotr Indyk , Shyam Narayanan , David P. Woodruff

The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…

Data Analysis, Statistics and Probability · Physics 2009-09-29 Ilya Nemenman , William Bialek , Rob de Ruyter van Steveninck

A technique introduced by Indyk and Woodruff [STOC 2005] has inspired several recent advances in data-stream algorithms. We show that a number of these results follow easily from the application of a single probabilistic method called…

Data Structures and Algorithms · Computer Science 2011-04-26 Alexandr Andoni , Robert Krauthgamer , Krzysztof Onak

We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…

Data Structures and Algorithms · Computer Science 2012-08-01 Cosmin Bonchis , Gabriel Istrate

We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…

Quantum Physics · Physics 2025-09-23 Idris Delsol , Omar Fawzi , Jan Kochanowski , Akshay Ramachandran

We consider the algorithm by Ferson et al. (Reliable computing 11(3), p. 207-233, 2005) designed for solving the NP-hard problem of computing the maximal sample variance over interval data, motivated by robust statistics (in fact, the…

Optimization and Control · Mathematics 2022-07-28 Miroslav Rada , Michal Černý , Ondřej Sokol

Estimating frequency moments of data streams is a very well studied problem and tight bounds are known on the amount of space that is necessary and sufficient when the stream is adversarially ordered. Recently, motivated by various…

Data Structures and Algorithms · Computer Science 2008-08-19 Alexandr Andoni , Andrew McGregor , Krzysztof Onak , Rina Panigrahy

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…

Optimization and Control · Mathematics 2019-10-22 Tobias Sutter , David Sutter , Peyman Mohajerin Esfahani , John Lygeros

Entropy and free-energy estimation are key in thermodynamic characterization of simulated systems ranging from spin models through polymers, colloids, protein structure, and drug-design. Current techniques suffer from being model specific,…

Statistical Mechanics · Physics 2019-10-30 Ram Avinery , Micha Kornreich , Roy Beck

Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…

Data Analysis, Statistics and Probability · Physics 2021-03-08 José M. Amigó , Roberto Dale , Piergiulio Tempesta

This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…

Data Structures and Algorithms · Computer Science 2020-03-10 Feras A. Saad , Cameron E. Freer , Martin C. Rinard , Vikash K. Mansinghka

Quantifying the complexity and irregularity of time series data is a primary pursuit across various data-scientific disciplines. Sample entropy (SampEn) is a widely adopted metric for this purpose, but its reliability is sensitive to the…

Applications · Statistics 2024-05-13 Zachary Blanks , Donald E. Brown

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

Information Theory · Computer Science 2021-11-29 Georg Pichler , Pablo Piantanida , Günther Koliander

We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that…

Computational Complexity · Computer Science 2019-02-05 Nikolaj Tatti