Posterior Consistency of the Silverman g-prior in Bayesian Model Choice

Part of Advances in Neural Information Processing Systems 21 (NIPS 2008)

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Authors

Zhihua Zhang, Michael Jordan, Dit-Yan Yeung

Abstract

<p>Kernel supervised learning methods can be unified by utilizing the tools from regularization theory. The duality between regularization and prior leads to interpreting regularization methods in terms of maximum a posteriori estimation and has motivated Bayesian interpretations of kernel methods. In this paper we pursue a Bayesian interpretation of sparsity in the kernel setting by making use of a mixture of a point-mass distribution and prior that we refer to as ``Silverman's g-prior.'' We provide a theoretical analysis of the posterior consistency of a Bayesian model choice procedure based on this prior. We also establish the asymptotic relationship between this procedure and the Bayesian information criterion.</p>