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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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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-02874192
Contributor : Thomas Lartigue <>
Submitted on : Tuesday, November 24, 2020 - 8:01:36 AM
Last modification on : Thursday, January 14, 2021 - 3:14:14 PM

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  • HAL Id : hal-02874192, version 2
  • ARXIV : 2006.11094

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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. 2020. ⟨hal-02874192v2⟩

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