# A unified construction for series representations and finite approximations of completely random measures

arXiv: https://arxiv.org/abs/1905.10733 · HTML: https://mlsanity.com/paper/1905.10733/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2019.

## 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)

Infinite-activity completely random measures (CRMs) have become important building blocks of complex Bayesian nonparametric models. They have been successfully used in various applications such as clustering, density estimation, latent feature models, survival analysis or network science. Popular infinite-activity CRMs include the (generalized) gamma process and the (stable) beta process. However, except in some specific cases, exact simulation or scalable inference with these models is challenging and finite-dimensional approximations are often considered. In this work, we propose a general and unified framework to derive both series representations and finite-dimensional approximations of CRMs. Our framework can be seen as an extension of constructions based on size-biased sampling of Poisson point process [Perman1992]. It includes as special cases several known series representations as well as novel ones. In particular, we show that one can get novel series representations for the generalized gamma process and the stable beta process. We also provide some analysis of the truncation error.