# Compound random measures and their use in Bayesian nonparametrics

arXiv: https://arxiv.org/abs/1410.0611 · HTML: https://mlsanity.com/paper/1410.0611/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2014.

## Built on by (most cited first, 2 of 2)

- [Deep neural networks with dependent weights: Gaussian Process mixture limit, heavy tails, sparsity and compressibility](https://mlsanity.com/paper/2205.08187/) (2022)
- [Rapidly Varying Completely Random Measures for Modeling Extremely Sparse Networks](https://mlsanity.com/paper/2505.13206/) (2025)

## Abstract (arXiv)

A new class of dependent random measures which we call it compound random measures are proposed and the use of normalized versions of these random measures as priors in Bayesian nonparametric mixture models is considered. Their tractability allows the properties of both compound random measures and normalized compound random measures to be derived. In particular, we show how compound random measures can be constructed with gamma, σ-stable and generalized gamma process marginals. We also derive several forms of the Laplace exponent and characterize dependence through both the L'evy copula and correlation function. A slice sampler and an augmented P'olya urn scheme sampler are described for posterior inference when a normalized compound random measure is used as the mixing measure in a nonparametric mixture model and a data example is discussed.