Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Multi-label informed latent semantic indexing
Proceedings of the 28th annual international ACM SIGIR conference on Research and development in information retrieval
Fast maximum margin matrix factorization for collaborative prediction
ICML '05 Proceedings of the 22nd international conference on Machine learning
Combining content and link for classification using matrix factorization
SIGIR '07 Proceedings of the 30th annual international ACM SIGIR conference on Research and development in information retrieval
Bayesian probabilistic matrix factorization using Markov chain Monte Carlo
Proceedings of the 25th international conference on Machine learning
Relational learning via collective matrix factorization
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Principal Component Analysis for Large Scale Problems with Lots of Missing Values
ECML '07 Proceedings of the 18th European conference on Machine Learning
Scalable Collaborative Filtering Approaches for Large Recommender Systems
The Journal of Machine Learning Research
Weighted Nonnegative Matrix Co-Tri-Factorization for Collaborative Prediction
ACML '09 Proceedings of the 1st Asian Conference on Machine Learning: Advances in Machine Learning
Posterior Cramer-Rao bounds for discrete-time nonlinear filtering
IEEE Transactions on Signal Processing
Matrix co-factorization on compressed sensing
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Connecting comments and tags: improved modeling of social tagging systems
Proceedings of the sixth ACM international conference on Web search and data mining
Hierarchical Bayesian matrix factorization with side information
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Matrix factorization is a popular method for collaborative prediction, where unknown ratings are predicted by user and item factor matrices which are determined to approximate a user-item matrix as their product. Bayesian matrix factorization is preferred over other methods for collaborative filtering, since Bayesian approach alleviates overfitting, integrating out all model parameters using variational inference or sampling methods. However, Bayesian matrix factorization still suffers from the cold-start problem where predictions of ratings for new items or of new users' preferences are required. In this paper we present Bayesian matrix co-factorization as an approach to exploiting side information such as content information and demographic user data, where multiple data matrices are jointly decomposed, i.e., each Bayesian decomposition is coupled by sharing some factor matrices. We derive variational inference algorithm for Bayesian matrix co-factorization. In addition, we compute Bayesian Cramér-Rao bound in the case of Gaussian likelihood, showing that Bayesian matrix co-factorization indeed improves the reconstruction over Bayesian factorization of single data matrix. Numerical experiments demonstrate the useful behavior of Bayesian matrix co-factorization in the case of cold-start problems.