Bayesian cluster analysis: Point estimation and credible balls

We propose Bayesian model averaging (BMA) as a method for postprocessing the results of model-based clustering. Given a number of competing models, appropriate model summaries are averaged, using the posterior model probabilities, instead of being taken from a single "best" model. We demonstrate the use of BMA in model-based clustering for a number of datasets. We show that BMA provides a useful summary of the clustering of observations while taking model uncertainty into acc...

Clustering stands as one of the most prominent challenges within the realm of unsupervised machine learning. Among the array of centroid-based clustering algorithms, the classic $k$-means algorithm, rooted in Lloyd's heuristic, takes center stage as one of the extensively employed techniques in the literature. Nonetheless, both $k$-means and its variants grapple with noteworthy limitations. These encompass a heavy reliance on initial cluster centroids, susceptibility to conve...

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial assumptions about the structure of data. Here we reformulate the clustering problem from an information theoretic perspective which avoids many of these assumptions. In particular, our formulation obviates the need for defining a cluster "protot...

Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on mixture model which is known as the EM algorithm where the parameters of the mixture model are usually estimated into a maximum likelihood estimation framework. Bayesian approach for finite and infinite Gaussian mixture model generates poi...

Bayesian model-based clustering is a widely applied procedure for discovering groups of related observations in a dataset. These approaches use Bayesian mixture models, estimated with MCMC, which provide posterior samples of the model parameters and clustering partition. While inference on model parameters is well established, inference on the clustering partition is less developed. A new method is developed for estimating the optimal partition from the pairwise posterior sim...

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for clustering probability distributions is the nested Dirichlet process, which however has the drawback of grouping distributions in a single cluster when ties are observed across samples. With the goal of achieving a flexible and effective clustering ...

We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based on maximizing mutual information between data and cluster labels. We demonstrate that this intuition suffers from a fundamental conceptual flaw that causes clustering performance to deteriorate as the amount of data increases. Instead, we re...

This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an assumed model (Gelman 2008). The Bayesian perspective is thus applicable to all aspects of statistical inference, while being open to the incorporation of information items resulting from earlier experiments and from expert opinions. We provide ...

Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to produce samples from the posterior distribution of the component labels. The data are then clustered by minimizing the expectation of a clustering loss function that favours similarity to the component labels. Unfortunately, although these...

Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In most cases the solution is explored via Monte Carlo sampling or variational methods. Here we work further on the application of variational methods to clustering problems. We introduce generative models based on a hidden group structure and...