# Bayesian Repulsive Gaussian Mixture Model

arXiv: https://arxiv.org/abs/1703.09061 · HTML: https://mlsanity.com/paper/1703.09061/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2017.

## Built on by (most cited first, 8 of 8)

- [Mean-field Variational Inference via Wasserstein Gradient Flow](https://mlsanity.com/paper/2207.08074/) (2022)
- [Why the Rich Get Richer? On the Balancedness of Random Partition Models](https://mlsanity.com/paper/2201.12697/) (2022)
- [A Bayesian Mixture Model of Temporal Point Processes with Determinantal Point Process Prior](https://mlsanity.com/paper/2411.04397/) (2024)
- [GEMSS: A Variational Method for Discovering Multiple Sparse Solutions in Classification and Regression Problems](https://mlsanity.com/paper/2602.08913/) (2026)
- [Scalable Posterior Uncertainty for Flexible Density-Based Clustering](https://mlsanity.com/paper/2603.03188/) (2026)
- [Posterior Regularization on Bayesian Hierarchical Mixture Clustering](https://mlsanity.com/paper/2105.06903/) (2021)
- [Entropy regularization in probabilistic clustering](https://mlsanity.com/paper/2307.10065/) (2023)
- [Sequential Adaptive Priors for Orthogonal Functions](https://mlsanity.com/paper/2508.15552/) (2025)

## Abstract (arXiv)

We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet process). The asymptotic results for the posterior distribution of the proposed models are derived, including posterior consistency and posterior contraction rate in the context of nonparametric density estimation. More importantly, we show that compared to the independent prior on the component centers, the repulsive prior introduces additional shrinkage effect on the tail probability of the posterior number of components, which serves as a measurement of the model complexity. In addition, an efficient and easy-to-implement blocked-collapsed Gibbs sampler is developed based on the exchangeable partition distribution and the corresponding urn model. We evaluate the performance and demonstrate the advantages of the proposed model through extensive simulation studies and real data analysis. The R code is available at https://drive.google.com/open?id=0B_zFse0eqxBHZnF5cEhsUFk0cVE.