The Sparsity-Constrained Graphical Lasso

Alessandro Fulci (), Sandra Paterlini and Emanuele Taufer
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Alessandro Fulci: University of Trento, Department of Economics and Management
Sandra Paterlini: University of Trento, Department of Economics and Management
Emanuele Taufer: University of Trento, Department of Economics and Management

A chapter in Mathematical and Statistical Methods for Actuarial Sciences and Finance, 2024, pp 172-178 from Springer

Abstract: Abstract This paper introduces the Sparsity-constrained Graphical Lasso (SCGlasso) for the precision matrix, $$\mathbf {\Theta }$$ Θ , in a multivariate Gaussian framework. The estimator is designed to produce a shrunk estimate of $$\mathbf {\Theta }$$ Θ , while simultaneously imposing a certain degree of sparsity, which is crucial for reconstructing the conditional dependence graph and the partial correlation graph. The proposed method employs an $$\ell _1$$ ℓ 1 -norm (Glasso) regularization to achieve shrinkage and imposes an $$\ell _0$$ ℓ 0 -pseudo-norm constraint to ensure sparsity. The proposed approach performs well compared to Glasso on simulated data, also in contexts where the number of variables p exceeds the number of observations n.

Keywords: Gaussian graphical models; Glasso; $$\ell _0$$ ℓ 0 -constraint; $$\ell _1$$ ℓ 1 -penalty (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-64273-9_29

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DOI: 10.1007/978-3-031-64273-9_29

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