Information Theoretic Learning: Renyi's Entropy and Kernel Perspectives

ISBN-13: 9781461425854 / Angielski / Miękka / 2012 / 448 str.

Jose C. Principe

Opis

This bookisan outgrowthoften yearsof researchatthe Universityof Florida Computational NeuroEngineering Laboratory (CNEL) in the general area of statistical signal processing and machine learning. One of the goals of writing the book is exactly to bridge the two ?elds that share so many common problems and techniques but are not yet e?ectively collaborating. Unlikeotherbooks thatcoverthe state ofthe artinagiven?eld, this book cuts across engineering (signal processing) and statistics (machine learning) withacommontheme: learningseenfromthepointofviewofinformationt- orywithanemphasisonRenyi'sde?nitionofinformation.Thebasicapproach is to utilize the information theory descriptors of entropy and divergence as nonparametric cost functions for the design of adaptive systems in unsup- vised or supervised training modes. Hence the title: Information-Theoretic Learning (ITL). In the course of these studies, we discovered that the main idea enabling a synergistic view as well as algorithmic implementations, does not involve the conventional central moments of the data (mean and covariance). Rather, the core concept is the ?-norm of the PDF, in part- ular its expected value (? = 2), which we call the information potential. This operator and related nonparametric estimators link information theory, optimization of adaptive systems, and reproducing kernel Hilbert spaces in a simple and unconventional way.

Recenzje

From the book reviews:

"The book is remarkable in various ways in the information it presents on the concept and use of entropy functions and their applications in signal processing and solution of statistical problems such as M-estimation, classification, and clustering. Students of engineering and statistics will greatly benefit by reading it." (C. R. Rao, Technometrics, Vol. 55 (1), February, 2013)

Spis treści

Information Theory, Machine Learning, and Reproducing Kernel Hilbert Spaces.- Renyi’s Entropy, Divergence and Their Nonparametric Estimators.- Adaptive Information Filtering with Error Entropy and Error Correntropy Criteria.- Algorithms for Entropy and Correntropy Adaptation with Applications to Linear Systems.- Nonlinear Adaptive Filtering with MEE, MCC, and Applications.- Classification with EEC, Divergence Measures, and Error Bounds.- Clustering with ITL Principles.- Self-Organizing ITL Principles for Unsupervised Learning.- A Reproducing Kernel Hilbert Space Framework for ITL.- Correntropy for Random Variables: Properties and Applications in Statistical Inference.- Correntropy for Random Processes: Properties and Applications in Signal Processing.

O autorze

José C. Principe is Distinguished Professor of Electrical and Biomedical Engineering, and BellSouth Professor at the University of Florida, and the Founder and Director of the Computational NeuroEngineering Laboratory. He is an IEEE and AIMBE Fellow, Past President of the International Neural Network Society, Past Editor-in-Chief of the IEEE Trans. on Biomedical Engineering and the Founder Editor-in-Chief of the IEEE Reviews on Biomedical Engineering. He has written an interactive electronic book on Neural Networks, a book on Brain Machine Interface Engineering and more recently a book on Kernel Adaptive Filtering, and was awarded the 2011 IEEE Neural Network Pioneer Award.

Blurb

This book presents the first cohesive treatment of Information Theoretic Learning (ITL) algorithms to adapt linear or nonlinear learning machines both in supervised or unsupervised paradigms. ITL is a framework where the conventional concepts of second order statistics (covariance, L2 distances, correlation functions) are substituted by scalars and functions with information theoretic underpinnings, respectively entropy, mutual information and correntropy.

ITL quantifies the stochastic structure of the data beyond second order statistics for improved performance without using full-blown Bayesian approaches that require a much larger computational cost. This is possible because of a non-parametric estimator of Renyi’s quadratic entropy that is only a function of pairwise differences between samples. The book compares the performance of ITL algorithms with the second order counterparts in many engineering and machine learning applications.

Students, practitioners and researchers interested in statistical signal processing, computational intelligence, and machine learning will find in this book the theory to understand the basics, the algorithms to implement applications, and exciting but still unexplored leads that will provide fertile ground for future research.

José C. Principe is Distinguished Professor of Electrical and Biomedical Engineering, and BellSouth Professor at the University of Florida, and the Founder and Director of the Computational NeuroEngineering Laboratory. He is an IEEE and AIMBE Fellow, Past President of the International Neural Network Society, Past Editor-in-Chief of the IEEE Trans. on Biomedical Engineering and the Founder Editor-in-Chief of the IEEE Reviews on Biomedical Engineering. He has written an interactive electronic book on Neural Networks, a book on Brain Machine Interface Engineering and more recently a book on Kernel Adaptive Filtering, and was awarded the 2011 IEEE Neural Network Pioneer Award.