A proximal distance algorithm for likelihood-based sparse covariance estimation. (16th February 2022)

• Record Type: Journal Article
• Authors: Xu, Jason; Lange, Kenneth
• Is Part Of: Biometrika. Volume 109:Number 4(2022)
• Page Start: 1047
• Page End: 1066
• Publication Date: 2022-02-16
• Subjects: Distance-to-set penalty -- Majorization-minimization -- Penalized likelihood -- Proximal algorithm -- Sequential unconstrained minimization -- Sparse estimation; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asac011
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes the distance from the covariance estimate to a symmetric sparsity set. This formulation avoids unwanted shrinkage induced by more common norm penalties, and enables optimization of the resulting nonconvex objective by solving a sequence of smooth, unconstrained subproblems. These subproblems are generated and solved via the proximal distance version of the majorization-minimization principle. The resulting algorithm executes rapidly, gracefully handles settings where the number of parameters exceeds the number of cases, yields a positive-definite solution, and enjoys desirable convergence properties. Empirically, we demonstrate that our approach outperforms competing methods across several metrics, for a suite of simulated experiments. Its merits are illustrated on international migration data and a case study on flow cytometry. Our findings suggest that the marginal and conditional dependency networks for the cell signalling data are more similar than previously concluded.