通过高效算法学习具有结构稀疏性的 hub graphical Lasso 模型
Learning the hub graphical Lasso model with the structured sparsity via an efficient algorithm
AI总结：
针对高维数据下带 hub 节点图模型拟合的计算难题，提出两阶段算法，结合 ADMM 与基于 SSN 的 ALM 挖掘稀疏结构，在保证高估计质量的同时大幅节省执行时间。
摘要：
图模型在从生物分析到推荐系统的众多任务中展现了其性能。然而，带有 hub 节点的图模型在拟合时计算困难，特别是当数据维度较大时。为了高效估计 hub graphical models，我们提出了一种两阶段算法。该算法首先通过双交替方向乘子法（ADMM）生成一个良好的初始点，然后热启动基于半光滑牛顿（SSN）的增广拉格朗日方法（ALM）来计算对于实际任务足够精确的解。我们充分挖掘了图模型中由 hubs 产生的广义雅可比矩阵的稀疏结构，确保算法能非常高效地获得良好的解。在合成数据和真实数据上的综合实验表明，它明显优于现有的最先进算法。特别是在一些高维任务中，它可以节省超过70%的执行时间，同时仍实现高质量的估计。
英文摘要：
Graphical models have exhibited their performance in numerous tasks ranging from biological analysis to recommender systems. However, graphical models with hub nodes are computationally difficult to fit, particularly when the dimension of the data is large. To efficiently estimate the hub graphical models, we introduce a two-phase algorithm. The proposed algorithm first generates a good initial point via a dual alternating direction method of multipliers (ADMM), and then warm starts a semismooth Newton (SSN) based augmented Lagrangian method (ALM) to compute a solution that is accurate enough for practical tasks. We fully excavate the sparsity structure of the generalized Jacobian arising from the hubs in the graphical models, which ensures that the algorithm can obtain a nice solution very efficiently. Comprehensive experiments on both synthetic data and real data show that it obviously outperforms the existing state-of-the-art algorithms. In particular, in some high dimensional tasks, it can save more than 70\% of the execution time, meanwhile still achieves a high-quality estimation.
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