2012/06/01 by Lingzhou Xue, Hui Zou, Tianxi Cai
Computer Science · Mathematics · Physics and Astronomy · #Antiretroviral drug #Bayesian Methods and Mixture Models #Complex Network Analysis Techniques #Estimation theory #Ising model #Oracle #Quasi-maximum likelihood #Statistical Methods and Inference #Statistical model #math.ST #stat.TH
paper · pdf · doi:10.1214/12-aos1017
published as Annals of Statistics 2012, Vol. 40, No. 3, 1403-1429 · Published in at http://dx.doi.org/10.1214/12-AOS1017 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2012/06/01 · arxiv created 2012/08/17 · arxiv updated 2012/08/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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.