Random Function Priors for Correlation Modeling

The likelihood model of high dimensional data Xn can often be expressed as p(Xn|Zn,θ), where θmathrelmathop:=(θk)k∈[K] is a collection of hidden features shared across objects, indexed by n, and Zn is a non-negative factor loading vector with K entries where Znk indicates the strength of θk used to express Xn. In this paper, we introduce random function priors for Zn for modeling correlations among its K dimensions Zn1 through ZnK, which we call textitpopulation random measure embedding (PRME). Our model can be viewed as a generalized paintbox model~citeBroderick13 using random functions, and can be learned efficiently with neural networks via amortized variational inference. We derive our Bayesian nonparametric method by applying a representation theorem on separately exchangeable discrete random measures.