The paper presents an efficient graph Laplacian estimation method based on the proximal Newton approach. The key contributions are:
Formulation of the graph Laplacian estimation problem as a nonconvex, Laplacian-constrained maximum likelihood estimation problem, using the minimax concave penalty (MCP) to promote sparsity.
Development of a proximal Newton method to solve this problem, which approximates the smooth part of the objective with a second-order Taylor expansion, while keeping the nonsmooth penalty and Laplacian constraints intact.
Introduction of several algorithmic novelties to efficiently solve the constrained Newton problem, including:
Theoretical analysis showing that the proposed method converges to a stationary point of the optimization problem.
Numerical experiments demonstrating the advantages of the proposed method in terms of both computational complexity and graph learning accuracy compared to existing methods, especially for problems with small sample sizes.
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by Yakov Medved... om arxiv.org 04-15-2024
https://arxiv.org/pdf/2302.06434.pdfDiepere vragen