Solomonoff's theory of inductive inference
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Solomonoff's theory of inductive inference is a mathematical theory of induction introduced by Ray Solomonoff, based on probability theory and theoretical computer science.[1][2][3] In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes' rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory.
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Solomonoff proved that this induction is incomputable, but noted that "this incomputability is of a very benign kind", and that it "in no way inhibits its use for practical prediction".[2]
Solomonoff's induction naturally formalizes Occam's razor[4][5][6][7][8] by assigning larger prior credences to theories that require a shorter algorithmic description.