Solomonoff's theory of inductive inference

Definition

Solomonoff's theory of inductive inference proves that, under its common sense assumptions (axioms), the best possible scientific model is the shortest algorithm that generates the empirical data under consideration. In addition to the choice of data, other assumptions are that, to avoid the post-hoc fallacy, the programming language must be chosen prior to the data and that the environment being observed is generated by an unknown algorithm. This is also called a theory of induction. Due to its basis in the dynamical character of Algorithmic Information Theory, it encompasses statistical as well as dynamical information criteria for model selection. It was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. 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.

Related concepts

AIXI Algorithmic Information Theory Algorithmic information theory Algorithmic probability Bayes' theorem Bayesian inference Bayesian probability Bit array Carl Herbert Smith Computability Computable Computably enumerable set Computer science Countable set E. Mark Gold Expected value Incomputable Inductive inference Inductive probability Inductive reasoning Infinite set Kolmogorov complexity Kullback–Leibler divergence Language identification in the limit Limit (math)MIT Press Marcus Hutter Martin Davis (mathematician)Mill's methods Minimum description length Minimum message length Model selection New riddle of induction No free lunch theorem Occam's razor Posterior probability Principle of Multiple Explanations Prior probability Probability Probability theory Problem of induction Programming language Ray Solomonoff Scientific theory State-space representation Stephen C. Kleene Super-recursive algorithm Universal artificial intelligence Universal computer William Gasarch Without loss of generality

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