Sparse Steinian Covariance Estimation

作者：Naul Brett^*; Taylor Jonathan

来源：Journal of Computational and Graphical Statistics, 2017, 26(2): 355-366.

DOI：10.1080/10618600.2016.1209117

• Covariance graph
• Mathematical statistics
• Multivariate analysis
• Numerical optimization

We consider a new method for sparse covariance matrix estimation which is motivated by previous results for the so-called Stein-type estimators. Stein proposed a method for regularizing the sample covariance matrix by shrinking together the eigenvalues; the amount of shrinkage is chosen to minimize an unbiased estimate of the risk (UBEOR) under the entropy loss function. The resulting estimator has been shown in simulations to yield significant risk reductions over the maximum likelihood estimator. Our method extends the UBEOR minimization problem by adding an l(1) penalty on the entries of the estimated covariance matrix, which encourages a sparse estimate. For a multivariate Gaussian distribution, zeros in the covariance matrix correspond to marginal independences between variables. Unlike the l(1)-penalized Gaussian likelihood function, our penalized UBEOR objective is convex and can be minimized via a simple block coordinate descent procedure. We demonstrate via numerical simulations and an analysis of microarray data from breast cancer patients that our proposed method generally outperforms other methods for sparse covariance matrix estimation and can be computed efficiently even in high dimensions.

• 出版日期2017