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Information and Control
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An introduction to Kolmogorov complexity and its applications (2nd ed.)
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COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
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Journal of the ACM (JACM)
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Journal of Computer and System Sciences
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IEEE Transactions on Information Theory
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IEEE Transactions on Information Theory
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IEEE Transactions on Information Theory
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Statistics and Computing
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Information and Computation
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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 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.