# Search Algorithms and Loss Functions for Bayesian Clustering

arXiv: https://arxiv.org/abs/2105.04451 · HTML: https://mlsanity.com/paper/2105.04451/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2021.

## Built on by (most cited first, 9 of 9)

- [Summarizing Bayesian Nonparametric Mixture Posterior -- Sliced Optimal Transport Metrics for Gaussian Mixtures](https://mlsanity.com/paper/2411.14674/) (2024)
- [Unsupervised Statistical Learning for Die Analysis in Ancient Numismatics](https://mlsanity.com/paper/2112.00290/) (2021)
- [Weighted Conformal Clustering](https://mlsanity.com/paper/2606.00436/) (2026)
- [Bayesian nonparametric mixture inconsistency for the number of components: How worried should we be in practice?](https://mlsanity.com/paper/2207.14717/) (2022)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [Scalable Posterior Uncertainty for Flexible Density-Based Clustering](https://mlsanity.com/paper/2603.03188/) (2026)
- [Vertical Consensus Inference for High-Dimensional Random Partition](https://mlsanity.com/paper/2603.27864/) (2026)
- [Entropy regularization in probabilistic clustering](https://mlsanity.com/paper/2307.10065/) (2023)
- [Bayesian temporal biclustering with applications to multi-subject neuroscience studies](https://mlsanity.com/paper/2406.17131/) (2024)

## Abstract (arXiv)

We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the minimization of the posterior expected loss is challenging. Our approach is a stochastic search based on a series of greedy optimizations performed in a random order and is embarrassingly parallel. We consider several loss functions, including Binder loss and variation of information. We note that criticisms of Binder loss are the result of using equal penalties of misclassification and we show an efficient means to compute Binder loss with potentially unequal penalties. Furthermore, we extend the original variation of information to allow for unequal penalties and show no increased computational costs. We provide a reference implementation of our algorithm. Using a variety of examples, we show that our method produces clustering estimates that better minimize the expected loss and are obtained faster than existing methods.