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Related papers: Information entropy of complex probability

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We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…

Adaptation and Self-Organizing Systems · Physics 2016-04-01 Guillermo Santamaría-Bonfil , Nelson Fernández , Carlos Gershenson

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

Methodology · Statistics 2024-07-19 Duncan K. Foley , Ellis Scharfenaker

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…

Machine Learning · Statistics 2023-11-01 David S. Watson , Joshua O'Hara , Niek Tax , Richard Mudd , Ido Guy

We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…

Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…

Quantum Physics · Physics 2015-02-24 Petr Jizba , Jacob A. Dunningham , Jaewoo Joo

The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…

Methodology · Statistics 2022-01-06 Stéphane Robin , Luca Scrucca

Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in…

Information Theory · Computer Science 2020-11-10 Christoph Hirche

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…

Mathematical Physics · Physics 2018-02-14 Demetris P. K. Ghikas , Fotios Oikonomou

Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…

Statistical Mechanics · Physics 2007-05-23 William Bialek , Naftali Tishby

The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Federico Milano

By 'informational entropy', we understand an inherent boundary to knowability, due e.g. to perceptual, theoretical, evidential or linguistic limits. In this paper, we discuss a logical framework in which this boundary is incorporated into…

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 thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…

Quantum Physics · Physics 2015-08-14 Marius Krumm

Choice overload occurs when individuals feel overwhelmed by an excessive number of options. Experimental evidence suggests that a larger selection can complicate the decision-making process. Consequently, choice satisfaction may diminish…

Physics and Society · Physics 2024-12-18 Mojtaba Madadi Asl , Kamal Hajian , Rouzbeh Torabi , Mehdi Sadeghi

It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…

Information Theory · Computer Science 2016-09-06 Kieran G. Larkin

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated…

Machine Learning · Computer Science 2026-03-17 Marc Finzi , Shikai Qiu , Yiding Jiang , Pavel Izmailov , J. Zico Kolter , Andrew Gordon Wilson

Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…

Statistics Theory · Mathematics 2026-02-16 Nicholas G. Polson , Daniel Zantedeschi

Information theory has been taken as a prospective tool for quantifying the complexity of complex networks. In this paper, we first study the information entropy or uncertainty of a path using the information theory. Then we apply the path…

Physics and Society · Physics 2016-05-04 Zhongqi Xu , Cunlai Pu , Jian Yang

In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…

Information Theory · Computer Science 2007-07-16 Alexander Shaydurov

Understanding the way in which random entities interact is of key interest in numerous scientific fields. This can range from a full characterization of the joint distribution to single scalar summary statistics. In this work we identify a…

Statistics Theory · Mathematics 2016-11-22 Yaniv Tenzer , Gal Elidan