English
Related papers

Related papers: Maximum Entropy Reconstruction for Discrete Distri…

200 papers

A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…

Methodology · Statistics 2024-05-09 Lucas Caparini , Gwynn J. Elfring , Mauricio Ponga

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

Statistics Theory · Mathematics 2019-11-12 Linda Altieri , Daniela Cocchi , Giulia Roli

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…

Analysis of PDEs · Mathematics 2013-11-08 U. Koley , N. H. Risebro , Ch. Schwab , F. Weber

This paper focuses on the problem of finding a distribution for an associated entropic vector in the entropy space nearest to a given, possibly non-entropic, target vector for random variables with a constraint on alphabet size. We show the…

Information Theory · Computer Science 2018-07-24 Sultan Alam , Satyajit Thakor , Syed Abbas

The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the…

Quantitative Methods · Quantitative Biology 2015-10-01 Alexander Andreychenko , Luca Bortolussi , Ramon Grima , Philipp Thomas , Verena Wolf

We present a new method for reconstructing two-dimensional mass maps of galaxy clusters from the image distortion of background galaxies. In contrast to most previous approaches, which directly convert locally averaged image ellipticities…

Astrophysics · Physics 2007-05-23 Stella Seitz , Peter Schneider , Matthias Bartelmann

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

Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…

Machine Learning · Statistics 2024-12-04 Wuyue Yang , Liangrong Peng , Guojie Li , Liu Hong

This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…

Probability · Mathematics 2025-07-16 Russel Cabasag , Samir Huq , Eric Mendoza , Mrinal Kanti Roychowdhury

Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…

Systems and Control · Electrical Eng. & Systems 2025-08-12 Alexandros E. Tzikas , Lukas Fiechtner , Arec Jamgochian , Mykel J. Kochenderfer

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…

Statistical Mechanics · Physics 2020-04-22 Gil Ariel , Yoram Louzoun

A vast concourse of events and phenomena occur in nature that may be interrelated by a entropy-maximization technique that provides a comprehensible explanation of a range of physical problems, integrating in a new framework the universal…

Classical Physics · Physics 2021-10-18 Mario J Pinheiro

Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…

Numerical Analysis · Mathematics 2007-11-06 Philippe G. LeFloch , Jian-Guo Liu

Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…

Statistical Mechanics · Physics 2015-10-05 Philipp Thomas , Ramon Grima

The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…

Data Analysis, Statistics and Probability · Physics 2009-11-10 Ariel Caticha , Roland Preuss

Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…

Numerical Analysis · Mathematics 2014-10-14 Andreychenko Alexander , Mikeev Linar , Wolf Verena

This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…

Information Theory · Computer Science 2016-11-17 Igal Sason

The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…

Computation · Statistics 2017-10-11 Brendon J. Brewer

Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…

Machine Learning · Statistics 2020-07-27 Tengyuan Liang , Weijie Su

This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…

Optimization and Control · Mathematics 2016-07-26 Xiaojun Lu , Yanhua Wu