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Communication Dans Un Congrès Année : 2023

Learning Graphical Factor Models with Riemannian Optimization

Résumé

Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within graph learning processes. This paper therefore addresses this issue by proposing a flexible algorithmic framework for graph learning under low-rank structural constraints on the covariance matrix. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution (a generalization of Gaussian graphical models to possibly heavy-tailed distributions), where the covariance matrix is optionally constrained to be structured as low-rank plus diagonal (low-rank factor model). The resolution of this class of problems is then tackled with Riemannian optimization, where we lever- age geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models. Numerical experiments on synthetic and real-world data sets illustrate the effectiveness of the proposed approach.
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hal-04249001 , version 1 (19-10-2023)

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Alexandre Hippert-Ferrer, Florent Bouchard, Ammar Mian, Titouan Vayer, Arnaud Breloy. Learning Graphical Factor Models with Riemannian Optimization. Joint European Conference on Machine Learning and Knowledge Discovery in Databases (ECML PKDD 2023), Sep 2023, Torino, Italy. ⟨10.1007/978-3-031-43421-1_21⟩. ⟨hal-04249001⟩
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