# Random Function Priors for Correlation Modeling

arXiv: https://arxiv.org/abs/1905.03826 · HTML: https://mlsanity.com/paper/1905.03826/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2019.

## Built on by (most cited first, 1 of 1)

- [Gaussian Process Tilted Nonparametric Density Estimation using Fisher Divergence Score Matching](https://mlsanity.com/paper/2504.03485/) (2025)

## Abstract (arXiv)

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.