Structured regularization for conditional Gaussian graphical models
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Conditional Gaussian graphical models are a reparametrization of the multivariate linear regression model which explicitly exhibits (i) the partial covariances between the predictors and the responses, and (ii) the partial covariances between the responses themselves. Such models are particularly suitable for interpretability since partial covariances describe direct relationships between variables. In this framework, we propose a regularization scheme to enhance the learning strategy of the model by driving the selection of the relevant input features by prior structural information. It comes with an efficient alternating optimization procedure which is guaranteed to converge to the global minimum. On top of showing competitive performance on artificial and real datasets, our method demonstrates capabilities for fine interpretation, as illustrated on three high-dimensional datasets from spectroscopy, genetics, and genomics.
KeywordsMultivariate regression Regularization Sparsity Conditional Gaussian graphical model Structured elastic net Regulatory motif QTL study Spectroscopy
We would like to thank Mathieu Lajoie and Laurent Bréhélin for kindly sharing the dataset from Gasch et al. (2000). We also thank the reviewers for their questions and remarks, which helped us to improve our manuscript. This project was conducted in the framework of the project AMAIZING funded by the French ANR. This work has been partially supported by the GRANT Reg4Sel from the French INRA-SelGen metaprogram.
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