Efficient Graph Laplacian Estimation by Proximal Newton
| Autor: | Medvedovsky, Yakov, Treister, Eran, Routtenberg, Tirza |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood estimation (MLE) of the precision matrix, subject to Laplacian structural constraints, with a sparsity-inducing penalty term. This paper aims to solve this learning problem accurately and efficiently. First, since the commonly used $\ell_1$-norm penalty is inappropriate in this setting and may lead to a complete graph, we employ the nonconvex minimax concave penalty (MCP), which promotes sparse solutions with lower estimation bias. Second, as opposed to existing first-order methods for this problem, we develop a second-order proximal Newton approach to obtain an efficient solver, utilizing several algorithmic features, such as using Conjugate Gradients, preconditioning, and splitting to active/free sets. Numerical experiments demonstrate the advantages of the proposed method in terms of both computational complexity and graph learning accuracy compared to existing methods. Comment: Proceedings of Artificial Intelligence and Statistics (AISTATS), 2024 |
| Databáze: | arXiv |
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