Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/93922
Title: | An efficient linearly convergent regularized proximal point algorithm for fused multiple graphical lasso problems | Authors: | Zhang, N Zhang, Y Sun, D Toh, KC |
Issue Date: | 2021 | Source: | SIAM journal on mathematics of data science, 2021, v. 3, no. 2, p. 524-543 | Abstract: | Nowadays, analyzing data from different classes or over a temporal grid has attracted a great deal of interest. As a result, various multiple graphical models for learning a collection of graphical models simultaneously have been derived by introducing sparsity in graphs and similarity across multiple graphs. This paper focuses on the fused multiple graphical Lasso model, which encourages not only shared pattern of sparsity but also shared values of edges across different graphs. For solving this model, we develop an efficient regularized proximal point algorithm, where the subproblem in each iteration of the algorithm is solved by a superlinearly convergent semismooth Newton method. To implement the semismooth Newton method, we derive an explicit expression for the generalized Jacobian of the proximal mapping of the fused multiple graphical Lasso regularizer. Unlike those widely used first order methods, our approach has heavily exploited the underlying second order information through the semismooth Newton method. This not only can accelerate the convergence of the algorithm but also can improve its robustness. The efficiency and robustness of our proposed algorithm are demonstrated by comparing it with some state-of-the-art methods on both synthetic and real data sets. | Keywords: | Fast linear convergence Network estimation Semismooth Newton method Sparse Jacobian |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on mathematics of data science | EISSN: | 2577-0187 | DOI: | 10.1137/20M1344160 | Rights: | © 2021 Society for Industrial and Applied Mathematics The following publication Zhang, N., Zhang, Y., Sun, D., & Toh, K. C. (2021). An efficient linearly convergent regularized proximal point algorithm for fused multiple graphical lasso problems. SIAM Journal on Mathematics of Data Science, 3(2), 524-543 is available at https://doi.org/10.1137/20M1344160 |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
20m1344160.pdf | 1.06 MB | Adobe PDF | View/Open |
Page views
52
Last Week
1
1
Last month
Citations as of May 5, 2024
Downloads
23
Citations as of May 5, 2024
WEB OF SCIENCETM
Citations
2
Citations as of May 2, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.