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Article Dans Une Revue IEEE Transactions on Pattern Analysis and Machine Intelligence Année : 2021

Gaussian Graphical Model exploration and selection in high dimension low sample size setting

Résumé

Gaussian graphical models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: the nodewise approach and the penalised likelihood maximisation. We demonstrate on synthetic data that, when the sample size is small, the two methods produce graphs with either too few or too many edges when compared to the real one. As a result, we propose a composite procedure that explores a family of graphs with a nodewise numerical scheme and selects a candidate among them with an overall likelihood criterion. We demonstrate that, when the number of observations is small, this selection method yields graphs closer to the truth and corresponding to distributions with better KL divergence with regards to the real distribution than the other two. Finally, we show the interest of our algorithm on two concrete cases: first on brain imaging data, then on biological nephrology data. In both cases our results are more in line with current knowledge in each field.
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Dates et versions

hal-02504034 , version 1 (10-03-2020)

Identifiants

Citer

Thomas Lartigue, Simona Bottani, Stephanie Baron, Olivier Colliot, Stanley Durrleman, et al.. Gaussian Graphical Model exploration and selection in high dimension low sample size setting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021, 43 (9), pp.3196-3213. ⟨10.1109/TPAMI.2020.2980542⟩. ⟨hal-02504034⟩
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