Bayesian Inference via Variational Approximation for Collaborative Filtering

Variational approximation method finds wide applicability in approximating difficult-to-compute probability distributions, a problem that is especially important in Bayesian inference to estimate posterior distributions. Latent factor model is a classical model-based collaborative filtering approach that explains the user-item association by characterizing both items and users on latent factors inferred from rating patterns. Due to the sparsity of the rating matrix, the latent factor model usually encounters the overfitting problem in practice. In order to avoid overfitting, it is necessary to use additional techniques such as regularizing the model parameters or adding Bayesian priors on parameters. In this paper, two generative processes of ratings are formulated by probabilistic graphical models with corresponding latent factors, respectively. The full Bayesian frameworks of such graphical models are proposed as well as the variational inference approaches for the parameter estimation. The experimental results show the superior performance of the proposed Bayesian approaches compared with the classical regularized matrix factorization methods.