Foundations of Induction - of Marcus Hutter

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Marcus Hutter - 20 - Foundations of InductionFoundations of Universal InductionOckhams’ razor (simplicity) principleEntities should not be multiplied beyond necessity.Epicurus’ principle of multiple explanationsIf more than one theory is consistent with the observations, keepall theories.Bayes’ rule for conditional probabilitiesGiven the prior belief/probability one can predict all future probabilities.Turing’s universal machineEverything computable by a human using a fixed procedure canalso be computed by a (universal) Turing machine.Kolmogorov’s complexityThe complexity or information content of an object is the lengthof its shortest description on a universal Turing machine.Solomonoff’s universal prior=Ockham+Epicurus+Bayes+TuringSolves the question of how to choose the prior if nothing is known.⇒ universal induction, formal Occam,AIT,MML,MDL,SRM,...
Marcus Hutter - 21 - Foundations of InductionScience ≈ Induction ≈ Occam’s Razor• Grue Emerald Paradox:Hypothesis 1: All emeralds are green.Hypothesis 2: All emeralds found till y2020 are green,thereafter all emeralds are blue.• Which hypothesis is more plausible? H1! Justification?• Occam’s razor: take simplest hypothesis consistent with data.is the most important principle in machine learning and science.• Problem: How to quantify “simplicity”? Beauty? Elegance?Description Length![The Grue problem goes much deeper. This is only half of the story]
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Foundations of Induction - of Marcus Hutter

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