A Bayesian Framework on Asymmetric Mixture of Factor Analyser

TL;DR

This paper introduces a Bayesian mixture of factor analyzers model using the flexible SUNGH distribution family, enabling better modeling of skewness and heavy tails in high-dimensional data with computational advantages.

Contribution

It proposes a novel Bayesian MFA model with SUNGH distributions, enhancing flexibility in modeling skewness and heavy tails, and demonstrating improved efficiency with real data and simulations.

Findings

Effective modeling of skewness and heavy tails in high-dimensional data.

Computational benefits due to the flexible density of SUNGH distributions.

Successful application to real data and simulations.

Abstract

Mixture of factor analyzer (MFA) model is an efficient model for the analysis of high dimensional data through which the factor-analyzer technique based on the covariance matrices reducing the number of free parameters. The model also provides an important methodology to determine latent groups in data. There are several pieces of research to extend the model based on the asymmetrical and/or with outlier datasets with some known computational limitations that have been examined in frequentist cases. In this paper, an MFA model with a rich and flexible class of skew normal (unrestricted) generalized hyperbolic (called SUNGH) distributions along with a Bayesian structure with several computational benefits have been introduced. The SUNGH family provides considerable flexibility to model skewness in different directions as well as allowing for heavy tailed data. There are several desirable properties in the structure of the SUNGH family, including, an analytically flexible density which leads to easing up the computation applied for the estimation of parameters. Considering factor analysis models, the SUNGH family also allows for skewness and heavy tails for both the error component and factor scores. In the present study, the advantages of using this family of distributions have been discussed and the suitable efficiency of the introduced MFA model using real data examples and simulation has been demonstrated.