  Latent Factor Model (LFM) is one of the most successful methods for
Collaborative filtering (CF) in the recommendation system, in which both users
and items are projected into a joint latent factor space. Base on matrix
factorization applied usually in pattern recognition, LFM models user-item
interactions as inner products of factor vectors of user and item in that space
and can be efficiently solved by least square methods with optimal estimation.
However, such optimal estimation methods are prone to overfitting due to the
extreme sparsity of user-item interactions. In this paper, we propose a
Bayesian treatment for LFM, named Bayesian Latent Factor Model (BLFM). Based on
observed user-item interactions, we build a probabilistic factor model in which
the regularization is introduced via placing prior constraint on latent
factors, and the likelihood function is established over observations and
parameters. Then we draw samples of latent factors from the posterior
distribution with Variational Inference (VI) to predict expected value. We
further make an extension to BLFM, called BLFMBias, incorporating
user-dependent and item-dependent biases into the model for enhancing
performance. Extensive experiments on the movie rating dataset show the
effectiveness of our proposed models by compared with several strong baselines.
