A Bayesian Treatment for Singular Value Decomposition

The traditional Singular Value Decomposition(SVD) based recommendation system suffers from two key chal-lenges, namely, (1) the normal assumption is not an appropriateone since it is sensitive to outliers, which means the predictedmean would be changed a lot from the true value by the presenceof outliers, and (2) the penalty terms added on the feature vectorsare difficult to be settled in advance and thus an automaticconfiguring method for setting penalty terms is indispensable. To solve that, we propose a Bayesian based singular valuedecomposition (BSVD) and its related inference algorithms inthis study. Specifically, we impose a T assumption on the ratingsand the feature vectors, and propose a Gibbs sampler for theinference part. Besides giving a statistical explanation of theinference part and showing that this procedure is meaningful, we list the results of a series of experiments to further verify theperformance of our proposed Bayesian SVD.