Foundations of Induction - of Marcus Hutter

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Marcus Hutter - 26 - Foundations of InductionInductive Inference & Universal Forecasting• Solomonoff combined Occam, Epicurus, Bayes, andTuring into one formal theory of sequential prediction.• M(x) = probability that a universal Turingmachine outputs x when provided withfair coin flips on the input tape.• A posteriori probability of y given x is M(y|x) = M(xy)/M(x).• Given x 1 , .., x t−1 , the probability of x t is M(x t |x 1 ...x t−1 ).• Immediate “applications”:- Weather forecasting: x t ∈ {sun,rain}.- Stock-market prediction: x t ∈ {bear,bull}.- Continuing number sequences in an IQ test: x t ∈ IN.• Optimal universal inductive reasoning system!
Marcus Hutter - 27 - Foundations of InductionSome Prediction Bounds for MM(x) = universal distribution. h n := ∑ x n(M(x n |x
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Foundations of Induction - of Marcus Hutter

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