Sequential Predictions based on Algorithmic Complexity

Details Sequential Predictions based on Algorithmic Complexity Sequential Predictions based on Algorithmic Complexity

2005-08-05

arxiv.org/abs/cs/0508043v1

Journal of Computer and System Sciences, 72:1 (2006) pages 95-117

Computer Science

Information Theory

26 pages, LaTeX

Scientific paper

This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff's universal 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 convergence can be slow. In probabilistic environments, neither the posterior nor the losses converge, in general.

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