Marcus Hutter - 1 - Universal Induction & Intelligence

Marcus Hutter - 1 - Universal Induction & Intelligence Foundations of Machine Learning Marcus Hutter Canberra, ACT, 0200, Australia http://www.hutter1.net/ ANU RSISE NICTA Machine Learning Summer School MLSS-2008, 2 { 15 March, Kioloa Marcus Hutter - 2 - Universal Induction & Intelligence Overview † Setup: Given (non)iid data D =(x ;:::;x ), predict x1 n n+1 † Ultimate goal is to maximize proflt or minimize loss † Consider Models/Hypothesis H 2Mi † Max.Likelihood: H =argmax p(DjH ) (overflts ifM large)best i i † Bayes: Posterior probability of H is p(HjD)/p(DjH )p(H )i i i i † Bayes needs prior(H )i † Occam+Epicurus: High prior for simple models. † Kolmogorov/Solomonofi: Quantiflcation of simplicity/complexity † Bayes works if D is sampled from H 2Mtrue † Universal AI = Universal Induction + Sequential Decision Theory Marcus Hutter - 3 - Universal Induction & Intelligence Abstract Machine learning is concerned with developing algorithms that learn from experience, build models of the environment from the acquired knowledge, and use these models for prediction. Machine learning is usually taught as a bunch of methods that can solve a bunch of problems (see my Introduction to SML last week). The following tutorial takes a step back and asks about the foundations of machine learning, in particular the (philosophical) problem of inductive inference, (Bayesian) statistics, and artiflcial intelligence. The tutorial concentrates on principled, unifled, and exact methods.