Approximate method of variational Bayesian matrix factorization with sparse prior

We study the problem of matrix factorization by variational Bayes method, under the assumption that observed matrix is the product of low-rank dense and sparse matrices with additional noise. Under assumption of Laplace distribution for sparse matrix prior, we analytically derive an approximate solution of matrix factorization by minimizing Kullback-Leibler divergence between posterior and trial function. By evaluating our solution numerically, we also discuss accuracy of matrix factorization of our analytical solution.