Overview
- Provides a developed theory that that is unique and specific rather than standard and average, and describes several cases such as discrete and continuous in a unified manner
- Contains the whole proofs but chooses the most simple and comprehensive ones
- Includes R codes and R packages (BNSL) for understanding the theory
Part of the book series: Behaviormetrics: Quantitative Approaches to Human Behavior (BQAHB, volume 25)
Buy print copy
Keywords
- Mutual Information
- Information Theory
- Nonparametric Estimation
- ICA
- Causality
- Chow Liu Algorithm
About this book
This book presents the mutual information (MI) estimation methods recently proposed by the author and published in a number of major journals. It includes two types of applications: learning a forest structure from data for multivariate variables and identifying independent variables (independent component analysis). MI between a pair of random variables is mathematically defined in information theory. It measures how dependent the two variables are, takes nonnegative values, and is zero if, and only if, they are independent, and is often necessary to know the value of MI between two variables in machine learning, statistical data analysis, and various sciences, including physics, psychology, and economics. However, the real value of MI is not available and it can only be estimated from data. The essential difference between this and other estimations is that consistency and independence testing are proved for the estimations proposed by the author, where the authors state that an estimation satisfies consistency and independence testing when the estimation corresponds to the true value and when the MI estimation value is zero with probability one as the sample size grows, respectively. Thus far, no MI estimations satisfy both these properties at once.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Estimation of Mutual Information
Authors: Joe Suzuki
Series Title: Behaviormetrics: Quantitative Approaches to Human Behavior
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2024
Hardcover ISBN: 978-981-13-0733-1Due: 11 August 2024
eBook ISBN: 978-981-13-0734-8Due: 11 August 2024
Series ISSN: 2524-4027
Series E-ISSN: 2524-4035
Edition Number: 1
Number of Pages: X, 120
Number of Illustrations: 40 b/w illustrations, 20 illustrations in colour