  We derive analytical expression of matrix factorization/completion solution
by variational Bayes method, under the assumption that observed matrix is
originally the product of low-rank dense and sparse matrices with additive
noise. We assume the prior of sparse matrix is Laplace distribution by taking
matrix sparsity into consideration. Then we use several approximations for
derivation of matrix factorization/completion solution. By our solution, we
also numerically evaluate the performance of sparse matrix reconstruction in
matrix factorization, and completion of missing matrix element in matrix
completion.
