Dynamic Bayesian Probabilistic Matrix Factorization

Collaborative filtering algorithms generally rely on the assumption that user preference patterns remain stationary. However, real-world relational data are seldom stationary. User preference patterns may change over time, giving rise to the requirement of designing collaborative filtering systems capable of detecting and adapting to preference pattern shifts. Motivated by this observation, in this paper we propose a dynamic Bayesian probabilistic matrix factorization model, designed for modeling time-varying distributions. Formulation of our model is based on imposition of a dynamic hierarchical Dirichlet process (dHDP) prior over the space of probabilistic matrix factorization models to capture the time-evolving statistical properties of modeled sequential relational datasets. We develop a simple Markov Chain Monte Carlo sampler to perform inference. We present experimental results to demonstrate the superiority of our temporal model.

[1]  Edward Y. Chang,et al.  Collaborative filtering for orkut communities: discovery of user latent behavior , 2009, WWW '09.

[2]  Arkadiusz Paterek,et al.  Improving regularized singular value decomposition for collaborative filtering , 2007 .

[3]  Lancelot F. James,et al.  Gibbs Sampling Methods for Stick-Breaking Priors , 2001 .

[4]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[5]  Michael I. Jordan,et al.  Variational inference for Dirichlet process mixtures , 2006 .

[6]  Max Welling,et al.  Multi-HDP: A Non Parametric Bayesian Model for Tensor Factorization , 2008, AAAI.

[7]  D. Blei,et al.  Truncation-free stochastic variational inference for Bayesian nonparametric models , 2012, NIPS 2012.

[8]  Xi Chen,et al.  Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization , 2010, SDM.

[9]  Bin Li,et al.  Tracking User-Preference Varying Speed in Collaborative Filtering , 2011, AAAI.

[10]  Ruslan Salakhutdinov,et al.  Probabilistic Matrix Factorization , 2007, NIPS.

[11]  Yehuda Koren,et al.  Collaborative filtering with temporal dynamics , 2009, KDD.

[12]  David B. Dunson,et al.  The dynamic hierarchical Dirichlet process , 2008, ICML '08.

[13]  Ruslan Salakhutdinov,et al.  Bayesian probabilistic matrix factorization using Markov chain Monte Carlo , 2008, ICML '08.

[14]  Michael I. Jordan,et al.  Hierarchical Dirichlet Processes , 2006 .

[15]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[16]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[17]  Xindong Wu,et al.  Cross-Domain Collaborative Filtering over Time , 2011, IJCAI.

[18]  Jing Pan,et al.  Robust probabilistic tensor analysis for time-variant collaborative filtering , 2013, Neurocomputing.

[19]  D. Blackwell,et al.  Ferguson Distributions Via Polya Urn Schemes , 1973 .

[20]  Tom Minka,et al.  Expectation Propagation for approximate Bayesian inference , 2001, UAI.