On Empirical Entropy
Information Theory
2011-04-05 v1 Machine Learning
math.IT
Abstract
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the description of the random variable involved plus the entropy it induces. We assume only that the distribution involved is computable. To test the new notion we compare the Normalized Information Distance (the similarity metric) with a related measure based on Mutual Information in Shannon's framework. This way the similarities and differences of the last two concepts are exposed.
Keywords
Cite
@article{arxiv.1103.5985,
title = {On Empirical Entropy},
author = {Paul M. B. Vitányi},
journal= {arXiv preprint arXiv:1103.5985},
year = {2011}
}
Comments
14 pages, LaTeX