Open Access
June 2012 Nonconcave penalized composite conditional likelihood estimation of sparse Ising models
Lingzhou Xue, Hui Zou, Tianxi Cai
Ann. Statist. 40(3): 1403-1429 (June 2012). DOI: 10.1214/12-AOS1017


The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose efficient procedures for learning a sparse Ising model based on a penalized composite conditional likelihood with nonconcave penalties. Nonconcave penalized likelihood estimation has received a lot of attention in recent years. However, such an approach is computationally prohibitive under high-dimensional Ising models. To overcome such difficulties, we extend the methodology and theory of nonconcave penalized likelihood to penalized composite conditional likelihood estimation. The proposed method can be efficiently implemented by taking advantage of coordinate-ascent and minorization–maximization principles. Asymptotic oracle properties of the proposed method are established with NP-dimensionality. Optimality of the computed local solution is discussed. We demonstrate its finite sample performance via simulation studies and further illustrate our proposal by studying the Human Immunodeficiency Virus type 1 protease structure based on data from the Stanford HIV drug resistance database. Our statistical learning results match the known biological findings very well, although no prior biological information is used in the data analysis procedure.


Download Citation

Lingzhou Xue. Hui Zou. Tianxi Cai. "Nonconcave penalized composite conditional likelihood estimation of sparse Ising models." Ann. Statist. 40 (3) 1403 - 1429, June 2012.


Published: June 2012
First available in Project Euclid: 10 August 2012

zbMATH: 1284.62451
MathSciNet: MR3015030
Digital Object Identifier: 10.1214/12-AOS1017

Primary: 62G20 , 62P10
Secondary: 90-08

Keywords: Composite likelihood , coordinatewise optimization , HIV drug resistance database , Ising model , minorization–maximization principle , NP-dimension asymptotic theory

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 3 • June 2012
Back to Top