Bayesian Robust PCA of Incomplete Data

Abstract

We present a probabilistic model for robust factor analysis and principal component analysis in which the observation noise is modeled by Student-t distributions in order to reduce the negative effect of outliers. The Student-t distributions are modeled independently for each data dimensions, which is different from previous works using multivariate Student-t distributions. We compare methods using the proposed noise distribution, the multivariate Student-t and the Laplace distribution. Intractability of evaluating the posterior probability density is solved by using variational Bayesian approximation methods. We demonstrate that the assumed noise model can yield accurate reconstructions because corrupted elements of a bad quality sample can be reconstructed using the other elements of the same data vector. Experiments on an artificial dataset and a weather dataset show that the dimensional independency and the flexibility of the proposed Student-t noise model can make it superior in some applications.