标题： 高斯图模型中最优估计的图形非凸优化 显示英文标题

标题： Graphical Nonconvex Optimization for Optimal Estimation in Gaussian Graphical Models

摘要： 我们研究了学习高维高斯图模型的问题。图形lasso是最受欢迎的估计高斯图模型的方法之一。然而，它不能达到最优收敛率。本文提出了一种用于高斯图模型最优估计的图形非凸优化方法，然后通过一系列凸规划对其进行近似。我们的提议是可计算的，并且生成的估计器可以达到最优收敛率。通过收缩性质，清楚地展示了使用凸规划进行顺序近似引入的统计误差。使用稀疏模式的概念可以进一步提高收敛率。然后将所提出的这种方法扩展到半参数图模型。通过数值研究表明，所提出的估计器比其他流行的估计高斯图模型的方法表现更好。 显示英文摘要

摘要： We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimation in Gaussian graphical models, which is then approximated by a sequence of convex programs. Our proposal is computationally tractable and produces an estimator that achieves the oracle rate of convergence. The statistical error introduced by the sequential approximation using the convex programs are clearly demonstrated via a contraction property. The rate of convergence can be further improved using the notion of sparsity pattern. The proposed methodology is then extended to semiparametric graphical models. We show through numerical studies that the proposed estimator outperforms other popular methods for estimating Gaussian graphical models.