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Optimality of Universal Bayesian Sequence Prediction for General Loss and Alphabet
Marcus Hutter
Various optimality properties of universal sequence predictors based on Bayes-mixtures in general, and Solomonoff's prediction scheme in particular, will be studied. The probabilit…
Bayesian Treatment of Incomplete Discrete Data applied to Mutual Information and Feature Selection
Marcus Hutter, Marco Zaffalon
Given the joint chances of a pair of random variables one can compute quantities of interest, like the mutual information. The Bayesian treatment of unknown chances involves comput…
Universal Sequential Decisions in Unknown Environments
Marcus Hutter
We give a brief introduction to the AIXI model, which unifies and overcomes the limitations of sequential decision theory and universal Solomonoff induction. While the former theor…
Hybrid Rounding Techniques for Knapsack Problems
Monaldo Mastrolilli, Marcus Hutter
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rou…
Updating beliefs with incomplete observations
Gert de Cooman, Marco Zaffalon
Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general,…