Sparse Gaussian graphical model estimation via alternating minimization
Sparse Gaussian graphical model estimation via alternating minimization
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DOI：
10.1093/biomet/asx003
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发表时间：
2014-05
期刊：
影响因子：
2.7
通讯作者：
Onkar Dalal;B. Rajaratnam
中科院分区：
文献类型：
--
作者：
Onkar Dalal;B. Rajaratnam
摘要近年来提出了几种利用逆协方差或精度矩阵的$\ell_{1}$正则化估计稀疏高斯图模型的方法。尽管最近取得了进展，但当代应用需要更快的方法来处理病态高维数据集。本文提出了一种利用交替最小化算法求解稀疏反协方差估计问题的新方法，该方法有效地作为对偶问题的近端梯度算法。我们的方法有几个优点：它比最先进的算法快很多个数量级；严密地证明了它的全局线性收敛性，强调了它良好的理论性质；它促进了基于领域特定知识的特征对之间的成对或边缘关系的附加约束；而且它更擅长处理条件极端恶劣的问题。在模拟数据集和真实数据集上均证明了该算法的准确性和速度。
SummarySeveral methods have recently been proposed for estimating sparse Gaussian graphical models using $\ell_{1}$-regularization on the inverse covariance or precision matrix. Despite recent advances, contemporary applications require even faster methods to handle ill-conditioned high-dimensional datasets. In this paper, we propose a new method for solving the sparse inverse covariance estimation problem using the alternating minimization algorithm, which effectively works as a proximal gradient algorithm on the dual problem. Our approach has several advantages: it is faster than state-of-the-art algorithms by many orders of magnitude; its global linear convergence has been rigorously demonstrated, underscoring its good theoretical properties; it facilitates additional constraints on pairwise or marginal relationships between feature pairs based on domain-specific knowledge; and it is better at handling extremely ill-conditioned problems. Our algorithm is shown to be more accurate and faster on simulated and real datasets.