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Solomonoff's theory of inductive inference
Solomonoff's theory of universal inductive inference is a theory of prediction based on logical observations, such as predicting the next symbol based upon a given series of symbols. The only assumption that the theory makes is that the environment follows some unknown but computable probability distribution. It is a mathematical formalization of Occam's razor〔JJ McCall. Induction: From Kolmogorov and Solomonoff to De Finetti and Back to Kolmogorov – Metroeconomica, 2004 – Wiley Online Library.〕〔D Stork. Foundations of Occam's razor and parsimony in learning from ricoh.com – NIPS 2001 Workshop, 2001〕〔A.N. Soklakov. Occam's razor as a formal basis for a physical theory
(from arxiv.org ) – Foundations of Physics Letters, 2002 – Springer〕〔M Hutter. On the existence and convergence of computable universal priors (arxiv.org ) – Algorithmic Learning Theory, 2003 – Springer〕 and the Principle of Multiple Explanations.〔Ming Li and Paul Vitanyi, ''An Introduction to Kolmogorov Complexity and Its Applications.'' Springer-Verlag, N.Y., 2008p 339 ff.〕
Prediction is done using a completely Bayesian framework. The universal prior is taken over the class of all computable sequences—this is the universal a priori probability distribution;
no computable hypothesis will have a zero probability. This means that Bayes rule of causation can be used in predicting the continuation of any particular computable sequence.
==Origin==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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