Latent Gaussian Graphical Models with Golazo Penalty

Ignacio Echave-Sustaeta Rodríguez, Frank Röttger
Proceedings of The 12th International Conference on Probabilistic Graphical Models, PMLR 246:199-212, 2024.

Abstract

The existence of latent variables in practical problems is common, for example when some variables are difficult or expensive to measure, or simply unknown. When latent variables are unaccounted for, structure learning for Gaussian graphical models can be blurred by additional correlation between the observed variables that is incurred by the latent variables. A standard approach for this problem is a latent version of the graphical lasso that splits the inverse covariance matrix into a sparse and a low-rank part that are penalized separately. In this paper we propose a generalization of this via the flexible Golazo penalty. This allows us to introduce latent versions of for example the adaptive lasso, positive dependence constraints or predetermined sparsity patterns, and combinations of those. We develop an algorithm for the latent Gaussian graphical model with the Golazo penalty and demonstrate it on simulated and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v246-echave-sustaeta-rodriguez24a, title = {Latent Gaussian Graphical Models with Golazo Penalty}, author = {Echave-Sustaeta Rodr{\'i}guez, Ignacio and R{\"o}ttger, Frank}, booktitle = {Proceedings of The 12th International Conference on Probabilistic Graphical Models}, pages = {199--212}, year = {2024}, editor = {Kwisthout, Johan and Renooij, Silja}, volume = {246}, series = {Proceedings of Machine Learning Research}, month = {11--13 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v246/main/assets/echave-sustaeta-rodriguez24a/echave-sustaeta-rodriguez24a.pdf}, url = {https://proceedings.mlr.press/v246/echave-sustaeta-rodriguez24a.html}, abstract = {The existence of latent variables in practical problems is common, for example when some variables are difficult or expensive to measure, or simply unknown. When latent variables are unaccounted for, structure learning for Gaussian graphical models can be blurred by additional correlation between the observed variables that is incurred by the latent variables. A standard approach for this problem is a latent version of the graphical lasso that splits the inverse covariance matrix into a sparse and a low-rank part that are penalized separately. In this paper we propose a generalization of this via the flexible Golazo penalty. This allows us to introduce latent versions of for example the adaptive lasso, positive dependence constraints or predetermined sparsity patterns, and combinations of those. We develop an algorithm for the latent Gaussian graphical model with the Golazo penalty and demonstrate it on simulated and real data.} }
Endnote
%0 Conference Paper %T Latent Gaussian Graphical Models with Golazo Penalty %A Ignacio Echave-Sustaeta Rodríguez %A Frank Röttger %B Proceedings of The 12th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2024 %E Johan Kwisthout %E Silja Renooij %F pmlr-v246-echave-sustaeta-rodriguez24a %I PMLR %P 199--212 %U https://proceedings.mlr.press/v246/echave-sustaeta-rodriguez24a.html %V 246 %X The existence of latent variables in practical problems is common, for example when some variables are difficult or expensive to measure, or simply unknown. When latent variables are unaccounted for, structure learning for Gaussian graphical models can be blurred by additional correlation between the observed variables that is incurred by the latent variables. A standard approach for this problem is a latent version of the graphical lasso that splits the inverse covariance matrix into a sparse and a low-rank part that are penalized separately. In this paper we propose a generalization of this via the flexible Golazo penalty. This allows us to introduce latent versions of for example the adaptive lasso, positive dependence constraints or predetermined sparsity patterns, and combinations of those. We develop an algorithm for the latent Gaussian graphical model with the Golazo penalty and demonstrate it on simulated and real data.
APA
Echave-Sustaeta Rodríguez, I. & Röttger, F.. (2024). Latent Gaussian Graphical Models with Golazo Penalty. Proceedings of The 12th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 246:199-212 Available from https://proceedings.mlr.press/v246/echave-sustaeta-rodriguez24a.html.

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