# Overfitting Bayesian Mixtures of Factor Analyzers with an Unknown Number of Components

## TL;DR

This paper introduces an overfitting Bayesian mixture of factor analyzers with an unknown number of components, demonstrating its effectiveness in clustering high-dimensional correlated data using MCMC and information criteria.

## Contribution

It presents a novel Bayesian framework for overfitting mixtures of factor analyzers with fixed factors, addressing label switching and estimating the number of components and factors.

## Key findings

- Effective in clustering high-dimensional data
- Outperforms state-of-the-art software in simulations
- Successfully applied to real datasets

## Abstract

Recent advances on overfitting Bayesian mixture models provide a solid and straightforward approach for inferring the underlying number of clusters and model parameters in heterogeneous datasets. The applicability of such a framework in clustering correlated high dimensional data is demonstrated. For this purpose an overfitting mixture of factor analyzers is introduced, assuming that the number of factors is fixed. A Markov chain Monte Carlo (MCMC) sampler combined with a prior parallel tempering scheme is used to estimate the posterior distribution of model parameters. The optimal number of factors is estimated using information criteria. Identifiability issues related to the label switching problem are dealt by post-processing the simulated MCMC sample by relabelling algorithms. The method is benchmarked against state-of-the-art software for maximum likelihood estimation of mixtures of factor analyzers using an extensive simulation study. Finally, the applicability of the method is illustrated in publicly available data.