A Variational Bayes approach to Robust Principal Component Analysis.
Mentor: Cris Moore
Abstract: 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. We estimate the low-rank and sparse matrices via a variational Bayes approach. Finally, we test and compare our Bayesian model with alternative approaches on both synthetic and real-world examples.