We propose a nonparametric extension to the factor analysis problem using a beta process prior. This beta process factor analysis (BP-FA) model allows for a dataset to be decomposed into a linear combination of a sparse set of factors, providing information on the underlying structure of the observations. As with the Dirichlet process, the beta process is a fully Bayesian conjugate prior, which allows for analytical posterior calculation and straightforward inference. We derive a variational Bayes inference algorithm and demonstrate the model on the MNIST digits and HGDP-CEPH cell line panel datasets. 1.

We present a variational Bayesian inference algorithm for the stick-breaking construction of the beta process. We derive an alternate representation of the beta process that is amenable to variational inference, and present a bound relating the truncated beta process to its infinite counterpart. We assess performance on two matrix factorization problems, using a non-negative factorization model and a linear-Gaussian model. 1.

We show that the stick-breaking construction of the beta process due to Paisley et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction. 1