Slides in PDF - of Marcus Hutter
Slides in PDF - of Marcus Hutter
Slides in PDF - of Marcus Hutter
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<strong>Marcus</strong> <strong>Hutter</strong> - 38 - Universal Induction & Intelligence<br />
Bayesian Sequence Prediction: Summary<br />
• The aim <strong>of</strong> probability theory is to describe uncerta<strong>in</strong>ty.<br />
• Various sources and <strong>in</strong>terpretations <strong>of</strong> uncerta<strong>in</strong>ty:<br />
frequency, objective, and subjective probabilities.<br />
• They all respect the same rules.<br />
• General sequence prediction: Use known (subj.) Bayes mixture<br />
ξ = ∑ ν∈M w νν <strong>in</strong> place <strong>of</strong> unknown (obj.) true distribution µ.<br />
• Bound on the relative entropy between ξ and µ.<br />
⇒ posterior <strong>of</strong> ξ converges rapidly to the true posterior µ.<br />
• ξ is also optimal <strong>in</strong> a decision-theoretic sense w.r.t. any bounded<br />
loss function.<br />
• No structural assumptions on M and ν ∈ M.