Ian Porteous

AAAI Conference 2010 Conference Paper

Bayesian Matrix Factorization with Side Information and Dirichlet Process Mixtures

• Ian Porteous
• Arthur Asuncion
• Max Welling

Matrix factorization is a fundamental technique in machine learning that is applicable to collaborative filtering, information retrieval and many other areas. In collaborative filtering and many other tasks, the objective is to fill in missing elements 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 observations. The side information helps by adding observed entries to the factored matrices. We also introduce a nonparametric 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 latent 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. Incorporating rating information with gathered metadata information, our Bayesian approach outperforms other matrix factorization techniques even when using fewer dimensions.

AAAI Conference 2008 Conference Paper

Multi-HDP: A Non Parametric Bayesian Model for Tensor Factorization

• Ian Porteous

Matrix factorization algorithms are frequently used in the machine learning community to find low dimensional representations of data. We introduce a novel generative Bayesian probabilistic model for unsupervised matrix and tensor factorization. The model consists of several interacting LDA models, one for each modality. We describe an efficient collapsed Gibbs sampler for inference. We also derive the nonparametric form of the model where interacting LDA models are replaced with interacting HDP models. Experiments demonstrate that the model is useful for prediction of missing data with two or more modalities as well as learning the latent structure in the data.

NeurIPS Conference 2007 Conference Paper

Infinite State Bayes-Nets for Structured Domains

• Max Welling
• Ian Porteous
• Evgeniy Bart

A general modeling framework is proposed that unifies nonparametric-Bayesian models, topic-models and Bayesian networks. This class of infinite state Bayes nets (ISBN) can be viewed as directed networks of ‘hierarchical Dirichlet processes’ (HDPs) where the domain of the variables can be structured (e. g. words in documents or features in images). We show that collapsed Gibbs sampling can be done efficiently in these models by leveraging the structure of the Bayes net and using the forward-filtering-backward-sampling algorithm for junction trees. Existing models, such as nested-DP, Pachinko allocation, mixed membership sto- chastic block models as well as a number of new models are described as ISBNs. Two experiments have been performed to illustrate these ideas.

UAI Conference 2006 Conference Paper

Gibbs Sampling for (Coupled) Infinite Mixture Models in the Stick Breaking Representation

• Ian Porteous
• Alexander Ihler
• Padhraic Smyth
• Max Welling