Bayesian nonparametric poisson factorization for recommendation systems

We develop a Bayesian nonparametric Poisson factorization model for recommendation systems. Poisson factorization implicitly models each user's limited budget of attention (or money) that allows consumption of only a small subset of the available items. In our Bayesian nonparametric variant, the number of latent components is theoretically unbounded and effectively estimated when computing a posterior with observed user behavior data. To approximate the posterior, we develop an efficient variational inference algorithm. It adapts the dimensionality of the latent components to the data, only requires iteration over the user/item pairs that have been rated, and has computational complexity on the same order as for a parametric model with fixed dimensionality. We studied our model and algorithm with large real-world data sets of user-movie preferences. Our model eases the computational burden of searching for the number of latent components and gives better predictive performance than its parametric counterpart.