Premium
A coordinate descent algorithm for sparse positive definite matrix estimation
Author(s) -
Yuan Ting,
Wang Junhui
Publication year - 2013
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11185
Subject(s) - positive definite matrix , coordinate descent , positive definiteness , covariance matrix , mathematics , algorithm , estimation of covariance matrices , diagonal , matrix (chemical analysis) , covariance , cluster analysis , diagonal matrix , sparse matrix , mathematical optimization , computer science , statistics , eigenvalues and eigenvectors , physics , geometry , materials science , quantum mechanics , composite material , gaussian
This paper proposes a coordinate descent (CD) algorithm that can be used for estimating sparse positive definite matrices. Positive definite matrix estimation is frequently encountered in multivariate statistics, such as estimation of the precision and covariance matrices. The proposed CD algorithm proceeds in a forward stagewise fashion, and iteratively updates the current estimated matrix at either one diagonal entry or two symmetric off‐diagonal entries. To assure the positive definiteness of the estimated matrices, the updating step size needs to be appropriately determined based on a simple sufficient and necessary condition. Furthermore, as each iteration updates only one or two coordinates, the sparsity in the estimated matrix can be achieved by early stopping the iteration. Extensive numerical experiments are conducted to demonstrate the effectiveness of the CD algorithm for estimation of the precision and covariance matrices. The CD algorithm is further extended to graph clustering and delivers superior performance as well. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2013