Estimating Multiple Precision Matrices with Cluster Fusion Regularization
Abstract
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, jointly. 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 kmeans clustering problem. Blockwise updates for computing the sparse estimator require solving 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 uknown in practice.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2003.00371
 Bibcode:
 2020arXiv200300371P
 Keywords:

 Statistics  Machine Learning;
 Computer Science  Machine Learning;
 Statistics  Computation;
 Statistics  Methodology