Multi-HDP: a non parametric Bayesian model for tensor factorization

Abstract

Matrix factorization algorithms are frequently used in the ma-chine learning community to find low dimensional represen-tations of data. We introduce a novel generative Bayesian probabilistic model for unsupervised matrix and tensor fac-torization. The model consists of several interacting LDA models, one for each modality. We describe an efficient col-lapsed Gibbs sampler for inference. We also derive the non-parametric form of the model where interacting LDA mod-els 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.