Sequence Prediction Based on Monotone Complexity

  • Marcus Hutter
Conference paper

DOI: 10.1007/978-3-540-45167-9_37

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2777)
Cite this paper as:
Hutter M. (2003) Sequence Prediction Based on Monotone Complexity. In: Schölkopf B., Warmuth M.K. (eds) Learning Theory and Kernel Machines. Lecture Notes in Computer Science, vol 2777. Springer, Berlin, Heidelberg

Abstract

This paper studies sequence prediction based on the monotone Kolmogorov complexity Km = − logm, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff’s prior M, the latter being an excellent predictor in deterministic as well as probabilistic environments, where performance is measured in terms of convergence of posteriors or losses. Despite this closeness to M, it is difficult to assess the prediction quality of m, since little is known about the closeness of their posteriors, which are the important quantities for prediction. We show that for deterministic computable environments, the “posterior” and losses of m converge, but rapid convergence could only be shown on-sequence; the off-sequence behavior is unclear. In probabilistic environments, neither the posterior nor the losses converge, in general.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Marcus Hutter
    • 1
  1. 1.IDSIAManno-LuganoSwitzerland

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