Mixture of Conditional Gaussian Graphical Models for unlabelled heterogeneous populations in the presence of co-factors

TL;DR

This paper introduces a Mixture of Conditional Gaussian Graphical Models (CGGM) that accounts for external co-features affecting data, improving sub-population identification in heterogeneous data where traditional mixtures fail.

Contribution

It proposes a novel CGGM-based mixture model with a penalised EM algorithm to handle heterogeneous effects of co-features, enhancing sub-population clustering accuracy.

Findings

Successfully identifies sub-populations in synthetic data.

Effectively accounts for heterogenous co-feature influences in real data.

Outperforms traditional mixture models disrupted by co-feature effects.

Abstract

Conditional correlation networks, within Gaussian Graphical Models (GGM), are widely used to describe the direct interactions between the components of a random vector. In the case of an unlabelled Heterogeneous population, Expectation Maximisation (EM) algorithms for Mixtures of GGM have been proposed to estimate both each sub-population's graph and the class labels. However, we argue that, with most real data, class affiliation cannot be described with a Mixture of Gaussian, which mostly groups data points according to their geometrical proximity. In particular, there often exists external co-features whose values affect the features' average value, scattering across the feature space data points belonging to the same sub-population. Additionally, if the co-features' effect on the features is Heterogeneous, then the estimation of this effect cannot be separated from the sub-population identification. In this article, we propose a Mixture of Conditional GGM (CGGM) that subtracts the heterogeneous effects of the co-features to regroup the data points into sub-population corresponding clusters. We develop a penalised EM algorithm to estimate graph-sparse model parameters. We demonstrate on synthetic and real data how this method fulfils its goal and succeeds in identifying the sub-populations where the Mixtures of GGM are disrupted by the effect of the co-features.