Approximation of the two-part MDL code

Authors:
Pieter Adriaans;Paul M. B. Vitányi
Affiliations:
Computer Science Department, University of Amsterdam, Amsterdam, The Netherlands;CWI, Amsterdam, The Netherlands
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

Approximation of the optimal two-part minimum description length (MDL) code for given data, through successive monotonically length-decreasing two-part MDL codes, has the following properties: i) computation of each step may take arbitrarily long; ii) we may not know when we reach the optimum, or whether we will reach the optimum at all; iii) the sequence of models generated may not monotonically improve the goodness of fit; but iv) the model associated with the optimum has (almost) the best goodness of fit. To express the practically interesting goodness of fit of individual models for individual data sets we have to rely on Kolmogorov complexity.