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Accelerated Path-Following Iterative Shrinkage Thresholding Algorithm With Application to Semiparametric Graph Estimation
Journal of Computational and Graphical Statistics ( IF 2.4 ) Pub Date : 2016-10-01 , DOI: 10.1080/10618600.2016.1164533
Tuo Zhao 1 , Han Liu 2
Affiliation  

We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high-dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, though simple, has profound impact: APISTA not only enjoys the same theoretical guarantee as that of PISTA, that is, APISTA attains a linear rate of convergence to a unique sparse local optimum with good statistical properties, but also significantly outperforms PISTA in empirical benchmarks. As an application, we apply APISTA to solve a family of nonconvex optimization problems motivated by estimating sparse semiparametric graphical models. APISTA allows us to obtain new statistical recovery results that do not exist in the existing literature. Thorough numerical results are provided to back up our theory.

中文翻译:

加速路径跟踪迭代收缩阈值算法在半参数图估计中的应用

我们提出了一种加速路径跟随迭代收缩阈值算法 (APISTA),用于解决高维稀疏非凸学习问题。APISTA 与路径跟踪迭代收缩阈值算法 (PISTA) 之间的主要区别在于 APISTA 利用额外的坐标下降子程序来提高计算性能。这样的修改虽然简单,但影响深远:APISTA 不仅享有与 PISTA 相同的理论保证,即 APISTA 获得线性收敛到具有良好统计特性的唯一稀疏局部最优,而且显着优于 PISTA在经验基准中。作为一个应用程序,我们应用 APISTA 来解决一系列由估计稀疏半参数图形模型驱动的非凸优化问题。APISTA 使我们能够获得现有文献中不存在的新统计恢复结果。提供了完整的数值结果来支持我们的理论。
更新日期:2016-10-01
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