Slides in PDF - of Marcus Hutter

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Marcus Hutter - 18 - Universal Induction & Intelligence BAYESIAN SEQUENCE PREDICTION • Sequential/Online Prediction – Setup • Uncertainty and Probability • Frequency Interpretation: Counting • Objective Uncertain Events & Subjective Degrees of Belief • Bayes’ and Laplace’s Rules • The Bayes-mixture distribution • Predictive Convergence • Sequential Decisions and Loss Bounds • Generalization: Continuous Probability Classes • Summary
Marcus Hutter - 19 - Universal Induction & Intelligence Bayesian Sequence Prediction: Abstract The aim of probability theory is to describe uncertainty. There are various sources and interpretations of uncertainty. I compare the frequency, objective, and subjective probabilities, and show that they all respect the same rules, and derive Bayes’ and Laplace’s famous and fundamental rules. Then I concentrate on general sequence prediction tasks. I define the Bayes mixture distribution and show that the posterior converges rapidly to the true posterior by exploiting some bounds on the relative entropy. Finally I show that the mixture predictor is also optimal in a decision-theoretic sense w.r.t. any bounded loss function.
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Slides in PDF - of Marcus Hutter

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