On the Foundations of Universal Sequence Prediction

Details On the Foundations of Universal Sequence Prediction On the Foundations of Universal Sequence Prediction

2006-05-03

arxiv.org/abs/cs/0605009v1

Proc. 3rd Annual Conference on Theory and Applications of Models of Computation (TAMC 2006) pages 408-420

Computer Science

Learning

14 pages

Scientific paper

Solomonoff completed the Bayesian framework by providing a rigorous, unique, formal, and universal choice for the model class and the prior. We discuss in breadth how and in which sense universal (non-i.i.d.) sequence prediction solves various (philosophical) problems of traditional Bayesian sequence prediction. We show that Solomonoff's model possesses many desirable properties: Fast convergence and strong bounds, and in contrast to most classical continuous prior densities has no zero p(oste)rior problem, i.e. can confirm universal hypotheses, is reparametrization and regrouping invariant, and avoids the old-evidence and updating problem. It even performs well (actually better) in non-computable environments.

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