The Sparsity-Constrained Graphical Lasso

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.