Nonconcave penalized composite conditional likelihood estimation of sparse ising models

Lingzhou Xue, Hui Zou, Tianxi Cai

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1403-1429
Number of pages27
JournalAnnals of Statistics
Volume40
Issue number3
DOIs
StatePublished - Jun 1 2012

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Composite Likelihood
Conditional Likelihood
Ising Model
Penalized Likelihood
High-dimensional
Oracle Property
Drug Resistance
Statistical Learning
Ascent
Protease
Local Solution
Asymptotic Properties
Virus
Dimensionality
Penalty
Optimality
Data analysis
Simulation Study
Model-based
Methodology

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Nonconcave penalized composite conditional likelihood estimation of sparse ising models. / Xue, Lingzhou; Zou, Hui; Cai, Tianxi.

In: Annals of Statistics, Vol. 40, No. 3, 01.06.2012, p. 1403-1429.

Research output: Contribution to journalArticle

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