# Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data

arXiv: https://arxiv.org/abs/2302.09111 · HTML: https://mlsanity.com/paper/2302.09111/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 72 references that are in the map.
- First posted on arXiv 17 Feb 2023.

## Builds on (most cited first, 13 of 13)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Bayesian Pyramids: Identifiable Multilayer Discrete Latent Structure Models for Discrete Data](https://mlsanity.com/paper/2101.10373/) (2021)
- [Are Gibbs-type priors the most natural generalization of the Dirichlet process?](https://mlsanity.com/paper/1503.00163/) (2015)
- [The Dependent Dirichlet Process and Related Models](https://mlsanity.com/paper/2007.06129/) (2020)
- [Nonparametric Bayesian Negative Binomial Factor Analysis](https://mlsanity.com/paper/1604.07464/) (2016)
- [Graphical Gaussian Process Models for Highly Multivariate Spatial Data](https://mlsanity.com/paper/2009.04837/) (2020)
- [Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes](https://mlsanity.com/paper/2110.10082/) (2021)
- [Latent nested nonparametric priors](https://mlsanity.com/paper/1801.05048/) (2018)
- [Flexible clustering via hidden hierarchical Dirichlet priors](https://mlsanity.com/paper/2201.06994/) (2022)
- [Modeling with Normalized Random Measure Mixture Models](https://mlsanity.com/paper/1310.0260/) (2013)
- [A Common Atom Model for the Bayesian Nonparametric Analysis of Nested Data](https://mlsanity.com/paper/2008.07077/) (2020)
- [The semi-hierarchical Dirichlet Process and its application to clustering homogeneous distributions](https://mlsanity.com/paper/2005.10287/) (2020)
- [Bayesian Nonparametric Common Atoms Regression for Generating Synthetic Controls in Clinical Trials](https://mlsanity.com/paper/2201.00068/) (2021)

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

- [Bayesian Transfer Learning](https://mlsanity.com/paper/2312.13484/) (2023)
- [Learning discrete Bayesian networks with hierarchical Dirichlet shrinkage](https://mlsanity.com/paper/2509.13267/) (2025)

## Abstract (arXiv)

We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we propose a Bayesian nonparametric approach, termed graphical Dirichlet process, that jointly models the dependent group-specific random measures by assuming each random measure to be distributed as a Dirichlet process whose concentration parameter and base probability measure depend on those of its parent groups. The resulting joint stochastic process respects the Markov property of the directed acyclic graph that links the groups. We characterize the graphical Dirichlet process using a novel hypergraph representation as well as the stick-breaking representation, the restaurant-type representation, and the representation as a limit of a finite mixture model. We develop an efficient posterior inference algorithm and illustrate our model with simulations and a real grouped single-cell dataset.