Alpha-NML Universal Predictors

Inspired by Sibson’s alpha-mutual information, we introduce a new parametric class of universal predictors. This class interpolates two well-known predictors, the mixture estimator, that includes the Laplace and the Krichevsky-Trofimov predictors, and the Normalized Maximum Likelihood (NML) estimator. We point out some advantages of this class of predictors and study its performance in terms of known regret measures under logarithmic loss, in particular for the well-studied case of discrete memoryless sources.