# Latent nested nonparametric priors

arXiv: https://arxiv.org/abs/1801.05048 · HTML: https://mlsanity.com/paper/1801.05048/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2018.

## Built on by (most cited first, 4 of 4)

- [Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data](https://mlsanity.com/paper/2302.09111/) (2023)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [Entropy regularization in probabilistic clustering](https://mlsanity.com/paper/2307.10065/) (2023)
- [Rapidly Varying Completely Random Measures for Modeling Extremely Sparse Networks](https://mlsanity.com/paper/2505.13206/) (2025)

## Abstract (arXiv)

Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested processes and study the dependence structures they induce. Dependence ranges between homogeneity, corresponding to full exchangeability, and maximum heterogeneity, corresponding to (unconditional) independence across samples. The popular nested Dirichlet process is shown to degenerate to the fully exchangeable case when there are ties across samples at the observed or latent level. To overcome this drawback, inherent to nesting general discrete random measures, we introduce a novel class of latent nested processes. These are obtained by adding common and group-specific completely random measures and, then, normalising to yield dependent random probability measures. We provide results on the partition distributions induced by latent nested processes, and develop an Markov Chain Monte Carlo sampler for Bayesian inferences. A test for distributional homogeneity across groups is obtained as a by product. The results and their inferential implications are showcased on synthetic and real data.