Unitary Approximate Message Passing for Matrix Factorization

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 UAMP-MF. With proper priors imposed on the factor matrices, UAMP-MF can be used to solve a range of problems formulated as MF, such as dictionary learning, compressive sensing with matrix uncertainty, robust principal component analysis, etc. Numerical examples are provided to show that UAMP-MF significantly outperforms state-of-the-art algorithms in terms of computational complexity, recovery accuracy and robustness.