Nonparametric Bayesian Matrix Factorization

The Dirichlet process has emerged as an attractive model for
clustering, where the number of clusters in the data is
automatically inferred through Gibbs sampling. Here we explore a
nonparametric Bayesian model for matrix (or more generally tensor)
factorization where the number of factors is automatically
inferred from the data. The model is based on a number of
interacting hierarchical Dirichlet processes (HDPs), one for each
modality of the data. Inference is performed using a simple
extension of the Gibbs sampler for the HDP. The proposed method
provides probabilistic estimates (unlike techniques such as SVD
and NNMF), has an efficient inference algorithm (we can run it on
arrays with 100 million entries) and is very general (most data
can be meaningfully organized into a multi-way array).
Experimental results are still preliminary but show promise.
