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Computer Science > Information Theory

arXiv:1103.5985 (cs)
[Submitted on 30 Mar 2011]

Title:On Empirical Entropy

Authors:Paul M.B. Vitányi (CWI and University of Amsterdam)
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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.
Comments: 14 pages, LaTeX
Subjects: Information Theory (cs.IT); Machine Learning (cs.LG)
MSC classes: 68, 94
ACM classes: H.1; F.1; J.1
Cite as: arXiv:1103.5985 [cs.IT]
  (or arXiv:1103.5985v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1103.5985

Submission history

From: Paul Vitanyi [view email]
[v1] Wed, 30 Mar 2011 16:30:27 UTC (15 KB)
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