A Variational Bayes Approach to Robust Principal Component Analysis

We solve the Robust Principal Component Analysis problem: decomposing an observed matrix into a low-rank matrix plus a sparse matrix. Unlike alternative methods that approximate this l0 objective with an l1 objective and solve a convex optimization problem, we develop a corresponding generative model and solve a statistical inference problem. The main advantages of this approach is its ability to incorporate additional prior information when it exists and cope with missing data where it does not. Using a variational Bayes approach, we develop an algorithm the low-rank and sparse matrices. Finally, we test and compare our Bayesian model with alternative approaches on both synthetic and real-world examples.