SIAM Journal on Optimization, Volume 30, Issue 3, Page 2197-2220, January 2020.
Undirected graphical models have been especially popular for learning the conditional independence structure among a large number of variables where the observations are drawn independently and identically from the same distribution. However, many modern statistical problems would involve categorical data or time-varying data, which might follow different but related underlying distributions. In order to learn a collection of related graphical models simultaneously, various joint graphical models inducing sparsity in graphs and similarity across graphs have been proposed. In this paper, we aim to propose an implementable proximal point dual Newton algorithm (PPDNA) for solving the group graphical Lasso model, which encourages a shared pattern of sparsity across graphs. Though the group graphical Lasso regularizer is nonpolyhedral, the asymptotic superlinear convergence of our proposed method PPDNA can be obtained by leveraging on the local Lipschitz continuity of the Karush--Kuhn--Tucker solution mapping associated with the group graphical Lasso model. A variety of numerical experiments on real data sets illustrates that the PPDNA for solving the group graphical Lasso model can be highly efficient and robust.

中文翻译：

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求解组图形套索问题的近点对偶牛顿算法

SIAM优化杂志，第30卷，第3期，第2197-2220页，2020年1月。
对于学习大量变量之间的条件独立性结构而言，无向图模型尤其受欢迎，在这些变量中，观察值是从同一分布中独立且相同地绘制的。但是，许多现代统计问题都涉及分类数据或时变数据，它们可能遵循不同但相关的基础分布。为了同时学习相关图形模型的集合，已经提出了引起图形稀疏性和跨图形相似性的各种联合图形模型。在本文中，我们旨在提出一种可解决的近点对偶牛顿算法（PPDNA），以解决组图形化的套索模型，该模型鼓励跨图共享稀疏模式。尽管组图形化套索正则化器是非多面体的，可以利用与组图形化Lasso模型相关的Karush-Kuhn-Tucker解映射的局部Lipschitz连续性来获得我们提出的方法PPDNA的渐近超线性收敛。在真实数据集上进行的各种数值实验表明，用于求解组图形化套索模型的PPDNA可能高效且可靠。