Bayesian Probabilistic Matrix Factorization: A User Frequency Analysis
  Matrix factorization (MF) has become a common approach to collaborative filtering, due to ease of implementation and scalability to large data sets. Two existing drawbacks of the basic model is that it does not incorporate side information on either users or items, and assumes a common variance for all users. We extend the work of constrained probabilistic matrix factorization by deriving the Gibbs updates for the side feature vectors for items (Salakhutdinov and Minh, 2008). We show that this Bayesian treatment to the constrained PMF model outperforms simple MAP estimation. We also consider extensions to heteroskedastic precision introduced in the literature (Lakshminarayanan, Bouchard, and Archambeau, 2011). We show that this tends result in overfitting for deterministic approximation algorithms (ex: Variational inference) when the observed entries in the user / item matrix are distributed in an non-uniform manner. In light of this, we propose a truncated precision model. Our experimental results suggest that this model tends to delay overfitting. 
Cody Severinski, Ruslan Salakhutdinov
stat.ML