Prior specification via prior predictive matching: Poisson matrix factorization and beyond

Hyperparameter optimization for machine learning models is typically carried out by some sort of cross-validation procedure or global optimization, both of which require running the learning algorithm numerous times. We show that for Bayesian hierarchical models there is an appealing alternative that allows selecting good hyperparameters without learning the model parameters during the process at all, facilitated by the prior predictive distribution that marginalizes out the model parameters. We propose an approach that matches suitable statistics of the prior predictive distribution with ones provided by an expert and apply the general concept for matrix factorization models. For some Poisson matrix factorization models we can analytically obtain exact hyperparameters, including the number of factors, and for more complex models we propose a model-independent optimization procedure

Dynamic Collaborative Filtering With Compound Poisson Factorization

Model-based collaborative filtering (CF) analyzes user–item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most CF approaches assume that these latent factors are static; however, in most CF data, user preferences and item perceptions drift over time. Here, we propose a new conjugate and numerically stable dynamic matrix factorization (DCPF) based on hierarchical Poisson factorization that models the smoothly drifting latent factors using gamma-Markov chains. We propose a conjugate gamma chain construction that is numerically stable within our compound-Poisson framework. We then derive a scalable stochastic variational inference approach to estimate the parameters of our model. We apply our model to time-stamped ratings data sets from Netflix, Yelp, and Last.fm. We empirically demonstrate that DCPF achieves a higher predictive accuracy than state-of-the-art static and dynamic factorization algorithms