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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…
Sequence Prediction based on Monotone Complexity
Marcus Hutter
This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff…
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…
On the Existence and Convergence Computable Universal Priors
Marcus Hutter
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algo…
Robust Estimators under the Imprecise Dirichlet Model
Marcus Hutter
Walley's Imprecise Dirichlet Model (IDM) for categorical data overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practic…