Random Function Priors for Correlation Modeling [article]

Aonan Zhang, John Paisley
2019 arXiv   pre-print
The likelihood model of high dimensional data X_n can often be expressed as p(X_n|Z_n,θ), where θ:=(θ_k)_k∈[K] is a collection of hidden features shared across objects, indexed by n, and Z_n is a non-negative factor loading vector with K entries where Z_nk indicates the strength of θ_k used to express X_n. In this paper, we introduce random function priors for Z_n for modeling correlations among its K dimensions Z_n1 through Z_nK, which we call population random measure embedding (PRME). Our
more » ... el can be viewed as a generalized paintbox model Broderick13 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.
arXiv:1905.03826v2 fatcat:zvmgegsfljcxna42ivehm7zpwu