  We consider matrix factorization (MF) with certain constraints, which finds
wide applications in various areas. Leveraging variational inference (VI) and
unitary approximate message passing (UAMP), we develop a Bayesian approach to
MF with an efficient message passing implementation, called UAMPMF. With proper
priors imposed on the factor matrices, UAMPMF can be used to solve many
problems that can be formulated as MF, such as non negative matrix
factorization, dictionary learning, compressive sensing with matrix
uncertainty, robust principal component analysis, and sparse matrix
factorization. Extensive numerical examples are provided to show that UAMPMF
significantly outperforms state-of-the-art algorithms in terms of recovery
accuracy, robustness and computational complexity.
