Kolmogorov's structure function for probability models

Abstract

This work was inspired by the paper of Vereshchagin and Vitanyi, where Kolmogorov's unpublished work on his structure function and the associated minimal sufficient statistics decomposition in the algorithmic theory of information is studied. The extension of Kolmogorov's great ideas to probability model classes turns out to add a new chapter to the MDL theory, which also provides an alternative approach to Shannon's rate-distortion theory.