Robust Bayesian PCA with Student’s t-distribution: The variational inference approach

Principal component analysis (PCA) is a technique that is widely used for applications such as dimensionality reduction, image compression, feature extraction and data visualization. One of the key issues in the use of PCA for modelling is that it is very sensitive to outliers since its formulation is based on Gaussian density model. Lately, more heavy-tailed distribution (i.e., Student´s t-distribution) is introduced to increase the robustness of traditional PCA. But the robust version of PCA is expressed as the maximum likelihood solution of a probabilistic latent variable model. This reformulation raises the question of how to determine the optimal number of principal components to be retained. In this paper, we develop a Bayesian model selection approach to estimate the true dimensionality of the data. The proposed algorithm is based on a new Bayesian treatment of robust Student´s t-distribution PCA. A simple Expectation-Maximization (EM) solver is introduced to find approximate solutions for the model. Experiments show that the proposed model achieves simultaneous optimal dimensionality selection an.d accurate principal components recovery.