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Hidden Markov ProcessesTheory and Applications to Biology$
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M. Vidyasagar

Print publication date: 2014

Print ISBN-13: 9780691133157

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691133157.001.0001

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Introduction to Information Theory

Introduction to Information Theory

Chapter:
(p.45) Chapter Two Introduction to Information Theory
Source:
Hidden Markov Processes
Author(s):

M. Vidyasagar

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691133157.003.0002

This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random variable (or more precisely, the probability distribution of the random variable). When there are two or more random variables, it is worthwhile to study the conditional entropy of one random variable with respect to another. The last concept is relative entropy, also known as the Kullback–Leibler divergence, which measures the “disparity” between two probability distributions. The chapter first considers convex and concave functions before discussing the properties of the entropy function, conditional entropy, uniqueness of the entropy function, and the Kullback–Leibler divergence.

Keywords:   information theory, entropy, random variable, conditional entropy, relative entropy, Kullback–Leibler divergence, probability distribution, convex function, concave function, entropy function

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