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Journal Articles SN Computer Science Year : 2021

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

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.
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Dates and versions

hal-02874192 , version 1 (19-06-2020)
hal-02874192 , version 2 (24-11-2020)
hal-02874192 , version 3 (16-03-2021)
hal-02874192 , version 4 (02-04-2021)
hal-02874192 , version 5 (23-02-2022)

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Thomas Lartigue, Stanley Durrleman, Stéphanie Allassonnière. Mixture of Conditional Gaussian Graphical Models for unlabelled heterogeneous populations in the presence of co-factors. SN Computer Science, 2021, 2 (466), ⟨10.1007/s42979-021-00865-5⟩. ⟨hal-02874192v5⟩
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