Bayesian Robust PCA for Incomplete Data

We present a probabilistic model for robust principal component analysis (PCA) in which the observation noise is modelled by Student-t distributions that are independent for different data dimensions. A heavy-tailed noise distribution is used to reduce the negative effect of outliers. Intractability of posterior evaluation is solved using variational Bayesian approximation methods. We show experimentally that the proposed model can be a useful tool for PCA preprocessing for incomplete noisy data. We also demonstrate that the assumed noise model can yield more accurate reconstructions of missing values: Corrupted dimensions of a "bad" sample may be reconstructed well from other dimensions of the same data vector. The model was motivated by a real-world weather dataset which was used for comparison of the proposed technique to relevant probabilistic PCA models.