Slides in PDF - of Marcus Hutter

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Marcus Hutter - 38 - Universal Induction & Intelligence Bayesian Sequence Prediction: Summary • The aim of probability theory is to describe uncertainty. • Various sources and interpretations of uncertainty: frequency, objective, and subjective probabilities. • They all respect the same rules. • General sequence prediction: Use known (subj.) Bayes mixture ξ = ∑ ν∈M w νν in place of unknown (obj.) true distribution µ. • Bound on the relative entropy between ξ and µ. ⇒ posterior of ξ converges rapidly to the true posterior µ. • ξ is also optimal in a decision-theoretic sense w.r.t. any bounded loss function. • No structural assumptions on M and ν ∈ M.
Marcus Hutter - 39 - Universal Induction & Intelligence UNIVERSAL INDUCTIVE INFERENCE • Foundations of Universal Induction • Bayesian Sequence Prediction and Confirmation • Convergence and Decisions • How to Choose the Prior – Universal • Kolmogorov Complexity • How to Choose the Model Class – Universal • The Problem of Zero Prior • Reparametrization and Regrouping Invariance • The Problem of Old Evidence / New Theories • Universal is Better than Continuous Class • More Bounds / Stuff / Critique / Problems • Summary / Outlook / Literature
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