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A Generalized Predictive Criterion for Model Selection

Mario Trottini and Fulvio Spezzaferri

Abstract:

Given a sample of n i.i.d. observations generated from some unknown distribution F, assume that F belongs to one of two parametric models M₁, M₂, and that the estimation of the density of a future observation is of interest. San Martini and Spezzaferri (1984) proposed for this problem a predictive criterion based on the Kullback Leibler divergence between the estimate and the density of the future observation. In this paper a generalization of this criterion is presented both using a general class of divergences and relaxing the assumption that the true model belongs to M₁ or M₂.

Keywords: Model Selection, Gaussian Process, Loss Function, $\alpha$-divergences.

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