Poland, JanHutter, Marcus2015-09-012015-09-010929-0672http://hdl.handle.net/1885/15051We study the properties of the MDL (or maximum penalized complexity) estimator for Regression and Classification, where the underlying model class is countable. We show in particular a finite bound on the Hellinger losses under the only assumption that there is a ``true'' model contained in the class. This implies almost sure convergence of the predictive distribution to the true one at a fast rate. It corresponds to Solomonoff's central theorem of universal induction, however with a bound that is exponentially larger.© The Author(s)RegressionClassificationSequence PredictionMachine LearningMinimum Description LengthBayes Mixture2005-02