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Rate-distortion-perception theory generalizes Shannon's rate-distortion theory by introducing a constraint on the perceptual quality of the output. The perception constraint complements the conventional distortion constraint and aims to…

Information Theory · Computer Science 2022-04-14 Jun Chen , Lei Yu , Jia Wang , Wuxian Shi , Yiqun Ge , Wen Tong

Recently, a new type of set, named as random permutation set (RPS), is proposed by considering all the permutations of elements in a certain set. For measuring the uncertainty of RPS, the entropy of RPS is presented. However, the maximum…

Information Theory · Computer Science 2022-03-24 Jixiang Deng , Yong Deng

The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…

Information Theory · Computer Science 2018-04-03 Jorge F. Silva

In this letter we show that the Shore--Johnson axioms for Maximum Entropy Principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought. Apart from a formal side of the…

Statistical Mechanics · Physics 2019-04-03 Petr Jizba , Jan Korbel

In the first chapter of Shannon's "A Mathematical Theory of Communication," it is shown that the maximum entropy rate of an input process of a constrained system is limited by the combinatorial capacity of the system. Shannon considers…

Information Theory · Computer Science 2009-11-20 Georg Böcherer , Valdemar Cardoso da Rocha Junior , Cecilio Pimentel

We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…

Statistics Theory · Mathematics 2007-06-13 Peter D. Grunwald , A. Philip Dawid

In many real-world applications, data is not collected as one batch, but sequentially over time, and often it is not possible or desirable to wait until the data is completely gathered before analyzing it. Thus, we propose a framework to…

Machine Learning · Statistics 2018-03-09 Elizabeth Hou , Alfred O. Hero

MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the…

Applications · Statistics 2015-06-04 A. Hernando , A. Plastino

The minimal set of Shannon-type inequalities (referred to as elemental inequalities), plays a central role in determining whether a given inequality is Shannon-type. Often, there arises a situation where one needs to check whether a given…

Information Theory · Computer Science 2017-06-13 Satyajit Thakor , Terence Chan , Alex Grant

Direct evaluation of the rate-distortion function has rarely been achieved when it is strictly greater than its Shannon lower bound. In this paper, we consider the rate-distortion function for the distortion measure defined by an…

Information Theory · Computer Science 2013-02-27 Kazuho Watanabe

We present a framework to address a class of sequential decision making problems. Our framework features learning the optimal control policy with robustness to noisy data, determining the unknown state and action parameters, and performing…

Machine Learning · Computer Science 2022-01-20 Amber Srivastava , Srinivasa M Salapaka

A central problem in quantum resource theory is to give operational meaning to quantum resources that can provide clear advantages in certain physical tasks compared to the convex set of resource-free states. We propose to extend this basic…

Quantum Physics · Physics 2024-12-30 Sunho Kim , Chunhe Xiong , Junde Wu

We give an interpretation of the Maximum Entropy (MaxEnt) Principle in game-theoretic terms. Based on this interpretation, we make a formal distinction between different ways of {em applying/} Maximum Entropy distributions. MaxEnt has…

Artificial Intelligence · Computer Science 2013-01-18 Peter D. Grunwald

We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…

Quantum Physics · Physics 2016-05-17 Stephan Weis

The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…

Neurons and Cognition · Quantitative Biology 2017-06-02 Ulisse Ferrari , Tomoyuki Obuchi , Thierry Mora

We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…

Physics and Society · Physics 2020-03-17 Cornelia Metzig , Caroline Colijn

Understanding how network function constrains neural connectivity is a central challenge in neuroscience. An influential approach is to train neural networks with gradient descent on cognitive tasks and characterize the resulting…

Neurons and Cognition · Quantitative Biology 2026-05-26 Ludwig Hruza , Srdjan Ostojic

A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is…

Information Theory · Computer Science 2015-10-20 Igal Sason , Sergio Verdu

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

Information Theory · Computer Science 2024-05-07 Mokshay Madiman , Prasad Tetali

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