# The Dependent Dirichlet Process and Related Models

arXiv: https://arxiv.org/abs/2007.06129 · HTML: https://mlsanity.com/paper/2007.06129/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2020.

## Built on by (most cited first, 7 of 7)

- [Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixtures](https://mlsanity.com/paper/2411.14674/) (2024)
- [Mixtures of Gaussian Process Experts with SMC2](https://mlsanity.com/paper/2208.12830/) (2022)
- [Graphical Dirichlet Process for Clustering Non-Exchangeable Grouped Data](https://mlsanity.com/paper/2302.09111/) (2023)
- [Dirichlet process mixture model based on topologically augmented signal representation for clustering infant vocalizations](https://mlsanity.com/paper/2407.05760/) (2024)
- [Mixtures of Gaussian process experts based on kernel stick-breaking processes](https://mlsanity.com/paper/2304.13833/) (2023)
- [Logistic-beta processes for dependent random probabilities with beta marginals](https://mlsanity.com/paper/2402.07048/) (2024)
- [The generalized underlap coefficient with an application in clustering](https://mlsanity.com/paper/2602.19473/) (2026)

## Abstract (arXiv)

Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate to assume a location/scale representation, where the error distribution has unchanging shape over the predictor space. In fact, it often happens in applied research that the distribution of responses under study changes with predictors in ways that cannot be reasonably represented by a finite dimensional functional form. This can seriously affect the answers to the scientific questions of interest, and therefore more general approaches are indeed needed. This gives rise to the study of fully nonparametric regression models. We review some of the main Bayesian approaches that have been employed to define probability models where the complete response distribution may vary flexibly with predictors. We focus on developments based on modifications of the Dirichlet process, historically termed dependent Dirichlet processes, and some of the extensions that have been proposed to tackle this general problem using nonparametric approaches.