Graphical Nonconvex Optimization via an Adaptive Convex Relaxation
Graphical Nonconvex Optimization via an Adaptive Convex Relaxation
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发表时间：
2018
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通讯作者：
Qiang Sun;Kean Ming Tan;Han Liu;Tong Zhang
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作者：
Qiang Sun;Kean Ming Tan;Han Liu;Tong Zhang
我们考虑了高维高斯图形模型的学习问题。图形套索是估计高斯图形模型最常用的方法之一。然而，它没有达到先知的收敛速度。本文提出了高斯图模型中最优估计的图解非凸优化问题，并用一系列自适应凸规划进行了逼近。我们的建议在计算上是容易处理的，并产生了一个达到先知收敛速度的估计器。序列近似引入的统计误差通过一个压缩性质被清楚地证明。然后将所提出的方法扩展到半参数图形模型的建模。我们通过数值研究表明，所提出的估计器的性能优于其他常用的估计高斯图模型的方法。
We consider the problem of learning highdimensional 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 adaptive 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 is clearly demonstrated via a contraction property. The proposed methodology is then extended to modeling semiparametric graphical models. We show via numerical studies that the proposed estimator outperforms other popular methods for estimating Gaussian graphical models.