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Graphical Elastic Net and Target Matrices: Fast Algorithms and Software for Sparse Precision Matrix Estimation

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arxiv 2101.02148 v1 pith:KHLJ2MDX submitted 2021-01-06 stat.ME stat.CO

Solt Kovács , Tobias Ruckstuhl , Helena Obrist , Peter Bühlmann This is my paper · ORCID
classification stat.MEstat.CO
keywords graphicalmatrixprecisionlassosoftwarealgorithmscorrespondingelastic
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abstract

We consider estimation of undirected Gaussian graphical models and inverse covariances in high-dimensional scenarios by penalizing the corresponding precision matrix. While single $L_1$ (Graphical Lasso) and $L_2$ (Graphical Ridge) penalties for the precision matrix have already been studied, we propose the combination of both, yielding an Elastic Net type penalty. We enable additional flexibility by allowing to include diagonal target matrices for the precision matrix. We generalize existing algorithms for the Graphical Lasso and provide corresponding software with an efficient implementation to facilitate usage for practitioners. Our software borrows computationally favorable parts from a number of existing packages for the Graphical Lasso, leading to an overall fast(er) implementation and at the same time yielding also much more methodological flexibility.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. High-dimensional Statistics Applications to Batch Effects in Metabolomics

    stat.ME 2024-12 reject novelty 4.0 of 10

    A new QC-based simultaneous test (QC-ST) and a covariance correction method (CoCo) are proposed to evaluate and reduce batch effects in metabolomics.

  2. Entropy Adjusted Graphical Lasso for Sparse Precision Matrix Estimation

    stat.ME 2025-01 reject novelty 1.0 of 10

    The proposed EAGL estimator adds a log-determinant penalty that duplicates the likelihood's own log-det term, making it equivalent to a scaled Graphical Lasso.

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