# Powered Dirichlet Process for Controlling the Importance of "Rich-Get-Richer" Prior Assumptions in Bayesian Clustering

arXiv: https://arxiv.org/abs/2104.12485 · HTML: https://mlsanity.com/paper/2104.12485/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 31 references that are in the map.
- First posted on arXiv 26 Apr 2021.

## Builds on (most cited first, 3 of 3)

- [Interactions in information spread: quantification and interpretation using stochastic block models](https://mlsanity.com/paper/2004.04552/) (2020)
- [Accurate and scalable social recommendation using mixed-membership stochastic block models](https://mlsanity.com/paper/1604.01170/) (2016)
- [Optimal prediction of decisions and model selection in social dilemmas using block models](https://mlsanity.com/paper/2004.12151/) (2020)

## Built on by (most cited first, 6 of 6)

- [Powered Hawkes-Dirichlet Process: Challenging Textual Clustering using a Flexible Temporal Prior](https://mlsanity.com/paper/2109.07170/) (2021)
- [Why the Rich Get Richer? On the Balancedness of Random Partition Models](https://mlsanity.com/paper/2201.12697/) (2022)
- [Multivariate Powered Dirichlet Hawkes Process](https://mlsanity.com/paper/2212.05995/) (2022)
- [Le Processus Powered Dirichlet-Hawkes comme A Priori Flexible pour Clustering Temporel de Textes](https://mlsanity.com/paper/2201.12568/) (2022)
- [Interactions in Information Spread](https://mlsanity.com/paper/2209.08026/) (2022)
- [Dirichlet-Survival Process: Scalable Inference of Topic-Dependent Diffusion Networks](https://mlsanity.com/paper/2212.05996/) (2022)

## Abstract (arXiv)

One of the most used priors in Bayesian clustering is the Dirichlet prior. It can be expressed as a Chinese Restaurant Process. This process allows nonparametric estimation of the number of clusters when partitioning datasets. Its key feature is the "rich-get-richer" property, which assumes a cluster has an a priori probability to get chosen linearly dependent on population. In this paper, we show that such prior is not always the best choice to model data. We derive the Powered Chinese Restaurant process from a modified version of the Dirichlet-Multinomial distribution to answer this problem. We then develop some of its fundamental properties (expected number of clusters, convergence). Unlike state-of-the-art efforts in this direction, this new formulation allows for direct control of the importance of the "rich-get-richer" prior.