The graphical lasso: new insights and alternatives. The graphical lasso [5] is an algorithm for learning the structure in an undirected Gaussian graphical model, using ℓ 1 regularization to control the number of zeros in the precision matrix Θ=Σ -1 [2, 11]. The R package glasso [5] is popular, fast, and allows one to efficiently build a path of models for different values of the tuning parameter. Convergence of glasso can be tricky; the converged precision matrix might not be the inverse of the estimated covariance, and occasionally it fails to converge with warm starts. In this paper we explain this behavior, and propose new algorithms that appear to outperform glasso. By studying the “normal equations” we see that, glasso is solving the dual of the graphical lasso penalized likelihood, by block coordinate ascent; a result which can also be found in [2]. In this dual, the target of estimation is Σ, the covariance matrix, rather than the precision matrix Θ. We propose similar primal algorithms p-glasso and dp-glasso, that also operate by block-coordinate descent, where Θ is the optimization target. We study all of these algorithms, and in particular different approaches to solving their coordinate sub-problems. We conclude that dp-glasso is superior from several points of view.

References in zbMATH (referenced in 430 articles , 1 standard article )

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  1. Barceló, Pablo; Baumgartner, Alexander; Dalmau, Victor; Kimelfeld, Benny: Regularizing conjunctive features for classification (2021)
  2. Bian, Fengmiao; Liang, Jingwei; Zhang, Xiaoqun: A stochastic alternating direction method of multipliers for non-smooth and non-convex optimization (2021)
  3. Burkina, M.; Nazarov, I.; Panov, M.; Fedonin, G.; Shirokikh, B.: Inductive matrix completion with feature selection (2021)
  4. Byrd, Michael; Nghiem, Linh H.; McGee, Monnie: Bayesian regularization of Gaussian graphical models with measurement error (2021)
  5. Fan, Xinyan; Zhang, Qingzhao; Ma, Shuangge; Fang, Kuangnan: Conditional score matching for high-dimensional partial graphical models (2021)
  6. Ha, Min Jin; Stingo, Francesco Claudio; Baladandayuthapani, Veerabhadran: Bayesian structure learning in multilayered genomic networks (2021)
  7. Huling, Jared D.; Smith, Maureen A.; Chen, Guanhua: A two-part framework for estimating individualized treatment rules from semicontinuous outcomes (2021)
  8. Kashlak, Adam B.: Non-asymptotic error controlled sparse high dimensional precision matrix estimation (2021)
  9. Kereta, Željko; Klock, Timo: Estimating covariance and precision matrices along subspaces (2021)
  10. Lapucci, Matteo; Levato, Tommaso; Sciandrone, Marco: Convergent inexact penalty decomposition methods for cardinality-constrained problems (2021)
  11. Laverny, Oskar; Masiello, Esterina; Maume-Deschamps, Véronique; Rullière, Didier: Dependence structure estimation using copula recursive trees (2021)
  12. Lee, Kyoungjae; Cao, Xuan: Bayesian inference for high-dimensional decomposable graphs (2021)
  13. Li, Yaguang; Xu, Wei; Gao, Xin: Graphical-model based high dimensional generalized linear models (2021)
  14. Lukemire, Joshua; Kundu, Suprateek; Pagnoni, Giuseppe; Guo, Ying: Bayesian joint modeling of multiple brain functional networks (2021)
  15. Ma, Cong; Lu, Junwei; Liu, Han: Inter-subject analysis: a partial Gaussian graphical model approach (2021)
  16. Musolas, Antoni; Smith, Steven T.; Marzouk, Youssef: Geodesically parameterized covariance estimation (2021)
  17. Obiang, Eunice Okome; Jézéquel, Pascal; Proïa, Frédéric: A partial graphical model with a structural prior on the direct links between predictors and responses (2021)
  18. Park, Gunwoong; Kim, Yesool: Learning high-dimensional Gaussian linear structural equation models with heterogeneous error variances (2021)
  19. Pham, Minh; Lin, Xiaodong; Ruszczyński, Andrzej; Du, Yu: An outer-inner linearization method for non-convex and nondifferentiable composite regularization problems (2021)
  20. Phan, Dzung T.; Menickelly, Matt: On the solution of (\ell_0)-constrained sparse inverse covariance estimation problems (2021)

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