Network Topology Inference with Sparsity and Laplacian Constraints

• URL: http://arxiv.org/abs/2309.00960v1
• Date: Sat, 2 Sep 2023 15:06:30 GMT
• Title: Network Topology Inference with Sparsity and Laplacian Constraints
• Authors: Jiaxi Ying, Xi Han, Rui Zhou, Xiwen Wang, Hing Cheung So
• Abstract summary: We tackle the network topology by utilizing Laplacian constrained Gaussian graphical models. We show that an efficient projection algorithm is developed to solve the resulting problem.
• Score: 18.447094648361453
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex} has uncovered the limitations of the widely used $\ell_1$-norm in learning sparse graphs under this model: empirically, the number of nonzero entries in the solution grows with the regularization parameter of the $\ell_1$-norm; theoretically, a large regularization parameter leads to a fully connected (densest) graph. To overcome these challenges, we propose a graph Laplacian estimation method incorporating the $\ell_0$-norm constraint. An efficient gradient projection algorithm is developed to solve the resulting optimization problem, characterized by sparsity and Laplacian constraints. Through numerical experiments with synthetic and financial time-series datasets, we demonstrate the effectiveness of the proposed method in network topology inference.

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