A Path Following Algorithm for Sparse Pseudo-Likelihood Inverse Covariance Estimation (SPLICE)
Abstract
Given n observations of a p-dimensional random vector, the covariance matrix and its inverse (precision matrix) are needed in a wide range of applications. Sample covariance (e.g. its eigenstructure) can misbehave when p is comparable to the sample size n. Regularization is often used to mitigate the problem. In this paper, we proposed an l1 penalized pseudo-likelihood estimate for the inverse covariance matrix. This estimate is sparse due to the l1 penalty, and we term this method SPLICE. Its regularization path can be computed via an algorithm based on the homotopy/LARS-Lasso algorithm. Simulation studies are carried out for various inverse covariance structures for p = 15 and n = 20; 1000. We compare SPLICE with the l1 penalized likelihood estimate and a l1 penalized Cholesky decomposition based method. SPLICE gives the best overall performance in terms of three metrics on the precision matrix and ROC curve for model selection. Moreover, our simulation results demonstrate that the SPLICE estimates are positive-definite for most of the regularization path even though the restriction is not enforced.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 24, 2008
- Accession Number
- ADA488563
Entities
People
- Bin Yu
- Guilherme V. Rocha
- Peng Zhao
Organizations
- University of California, Berkeley