An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Optimal Ordered Problem Solver
Machine Learning
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Universal Artificial Intelligence: Sequential Decisions Based On Algorithmic Probability
Statistical and Inductive Inference by Minimum Message Length (Information Science and Statistics)
Statistical and Inductive Inference by Minimum Message Length (Information Science and Statistics)
IEEE Transactions on Information Theory
Limits of learning about a categorical latent variable under prior near-ignorance
International Journal of Approximate Reasoning
Is there an elegant universal theory of prediction?
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
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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.