Bayesian clustering method captures noise and uncertainty precisely
Model-free Bayesian Clustering and Multimodal Posterior Summarisation
Machine Learning
Summary
Clustering means grouping similar things together, but it’s tricky when the data is noisy or doesn’t fit usual shapes well. This work introduces a new Bayesian way to create clusters without assuming a specific model, so it works well with irregular groups and noise. It also provides a way to summarize many possible groupings to understand different patterns clearly. This method avoids slow calculations typical in Bayesian methods and can run in parallel, making it faster. The authors show their technique accurately reflects uncertainty in clusters and noise.
What this means in practice
- •For data scientists: Generate parallelized, noise-aware cluster analyses without specifying explicit probabilistic models or costly sampling.
- •For biomedical data analysts: Summarize complicated clustering results from noisy, high-dimensional biological datasets with weighted representatives showing multiple cluster patterns.
Authors
Qing Li, Sara Wade
Abstract
We develop a model-free, noise-aware Bayesian clustering framework that constructs a martingale posterior over clusterings from a predictive Bayesian perspective. This avoids explicit likelihood-prior model specification, expensive MCMC sampling, and mode-seeking variational approximations, while accommodating irregular cluster shapes and enabling parallel generation of posterior draws. To interpret the posterior over high-dimensional, noise-aware clusterings, we introduce a Wasserstein-type summarization method. Using a novel noise-aware loss, this approach compresses the large collection of posterior draws into a small set of weighted representatives, capturing distinct cluster structures and noise assignments. Further, we marginalise the uncertainty in the density level, avoiding reliance on a specific choice. We establish theoretical properties of the proposed loss and guarantees for the level-marginal posterior approximation. Results demonstrate the framework's effectiveness in capturing clustering and noise uncertainty.