A variational method for learning sparse Bayesian regression

In this paper, comparing with the Gaussian prior, the Laplacian distribution which is a sparse distribution is employed as the weight prior in the relevance vector machine (RVM) which is a method for learning sparse regression and classification. In order to derive an expectation–maximization (EM) algorithm in closed form for learning the weights, a strict lower bound on the sparse distribution is employed in this paper. This strict lower bound conveniently gives a strict lower bound in Gaussian form for the weight posterior and thus naturally derives an EM algorithm in closed form for learning the weights and the hyperparameters.