Estimating Multiple Precision Matrices With Cluster Fusion Regularization
提出一个带惩罚的似然框架，同时估计多个类别的精度矩阵及其相互关系，通过交替凸优化和k均值聚类求解，模拟和实际数据表明优于忽略关系的方法。
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices or require this information be known a priori. The framework proposed in this article allows for simultaneous estimation of the precision matrices and relationships between the precision matrices. Sparse and nonsparse estimators are proposed, both of which require solving a nonconvex optimization problem. To compute our proposed estimators, we use an iterative algorithm which alternates between a convex optimization problem solved by blockwise coordinate descent and a k-means clustering problem. Blockwise updates for the sparse estimator require computing an elastic net penalized precision matrix estimation problem, which we solve using a proximal gradient descent algorithm. We prove that this subalgorithm has a linear rate of convergence. In simulation studies and two real data applications, we show that our method can outperform competitors that ignore relevant relationships between precision matrices and performs similarly to methods which use prior information often unknown in practice. Supplementary materials for this article are available online.