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An inexact interior point method for L1-regularized sparse covariance selection

Lu Li (lilu***at***nus.edu.sg)
Kim-Chuan Toh (mattohkc***at***nus.edu.sg)

Abstract: Sparse covariance selection problems can be formulated as log-determinant (log-det) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized inexact primal-dual path-following interior-point algorithm for solving large scale log-det SDP problems arising from sparse covariance selection problems. Our inexact algorithm solve the large and ill-conditioned linear system of equations in each iteration by a preconditioned iterative solver. By exploiting the structures in sparse covariance selection problems, we are able to design highly effective preconditioners to efficiently solve the large and ill-conditioned linear systems. Numerical experiments on both synthetic and real covariance selection problems show that our algorithm is highly efficient and outperforms other existing algorithms.

Keywords: log-determinant semidefinite programming, sparse inverse covariance selection, infeasible interior point method, inexact search direction, symmetric quasi-minimum residual iteration

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Applications -- Science and Engineering (Statistics )

Citation: National University of Singapore, February, 2010.

Download: [PDF]

Entry Submitted: 02/20/2010
Entry Accepted: 02/20/2010
Entry Last Modified: 11/17/2010

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