Estimating Multiple Precision Matrices With Cluster Fusion Regularization

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 or require this be known priori. The proposed in article allows simultaneous estimation of and matrices. Sparse nonsparse estimators are proposed, both which solving nonconvex optimization problem. To compute our estimators, we use an iterative algorithm alternates convex problem solved by blockwise coordinate descent k-means clustering Blockwise updates sparse estimator computing elastic net matrix problem, solve using proximal gradient algorithm. prove that subalgorithm has linear rate convergence. In simulation studies two real data applications, show method can outperform competitors ignore relevant performs similarly to prior often unknown practice. Supplementary materials available online.