Foundations of Induction - of Marcus Hutter
Foundations of Induction - of Marcus Hutter
Foundations of Induction - of Marcus Hutter
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<strong>Marcus</strong> <strong>Hutter</strong> - 25 - <strong>Foundations</strong> <strong>of</strong> <strong>Induction</strong>Algorithmic Probability Theory• Epicurus: If more than one theory is consistentwith the observations, keep all theories.• ⇒ uniform prior over all H i ?• Refinement with Occam’s razor quantifiedin terms <strong>of</strong> Kolmogorov complexity:P (H i ) := w U H i:= 2 −K T /U (H i )• Fixing T we have a complete theory for prediction.Problem: How to choose T .• Choosing U we have a universal theory for prediction.Observation: Particular choice <strong>of</strong> U does not matter much.Problem: Incomputable.
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