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Title: Using cluster fusion regularization to estimate multiple precision matrices Authors:  Brad Price - West Virginia University (United States) [presenting]
Aaron Molstad - University of Florida (United States)
Ben Sherwood - University of Kansas (United States)
Abstract: A new penalized likelihood framework is discussed for estimating multiple precision matrices from different classes. This framework allows for simultaneous estimation of the precision matrices and groupings of the classes (i.e., clusters). Sparse and non-sparse estimators are proposed, both of which are solved using an iterative blockwise coordinate descent algorithm. The algorithm iterates between estimating the precision matrices given the groups and estimating the clusters given the precision matrices. 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 relevant competitors which do not account for groupings of the classes, or do not account for similarity across classes.