PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Shannon Information and Kolmogorov Complexity
Peter Grünwald and Paul Vitányi
submitted 2004.


We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories: Shannon entropy versus Kolmogorov complexity, the relation of both to universal coding, Shannon mutual information versus Kolmogorov (`algorithmic') mutual information, probabilistic sufficient statistic versus algorithmic sufficient statistic (related to lossy compression in the Shannon theory versus meaningful information in the Kolmogorov theory), and rate distortion theory versus Kolmogorov's structure function. Part of the material has appeared in print before, scattered through various publications, but this is the first comprehensive systematic comparison. The last mentioned relations are new.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:322
Deposited By:Peter Grünwald
Deposited On:09 December 2004