Bayesian Matrix Factorization with Side Information and Dirichlet Process Mixtures.pdf

Bayesian Matrix Factorization with Side Information and Dirichlet Process Mixtures Ian Porteous and Arthur Asuncion and Max Welling Bren School of Information and Computer Science University of California Irvine Irvine, CA 92697 {iporteou,asuncion,welling}@ Abstract Matrix factorization is a fundamental technique in machine learning that is applicable to collaborative filtering, informa- tion retrieval and many other areas. In collaborative filtering and many other tasks, the objective is to fill in missing ele- ments of a sparse data matrix. One of the biggest challenges in this case is filling in a column or row of the matrix with very few observations. In this paper we introduce a Bayesian matrix factorization model that performs regression against side information known about the data in addition to the ob- servations. The side information helps by adding observed entries to the factored matrices. We also introduce a nonpara- metric mixture model for the prior of the rows and columns of the factored matrices that gives a different regularization for each latent class. Besides providing a richer prior, the posterior distribution of mixture assignments reveals the la- tent classes. Using Gibbs sampling for inference, we apply our model to the Netflix Prize problem of predicting movie ratings given an incomplete user-movie ratings matrix. In- corporating rating information with gathered metadata infor- mation, our Bayesian approach outperforms other matrix fac- torization techniques even when using fewer dimensions. Introduction Matrix factorization is an important technique in machine learning which has proven to be effective for collaborative filtering (Koren 2008), information retrieval (Deerwester et al. 1990), image analysis (Lee and Seung 1999), and many other areas. A drawback of standard matrix factor- ization algorithms is that they are susceptible to overfitting on the training data and require careful tuning of the regu- larization parameters and the num