Nonconcave penalized composite conditional likelihood estimation of sparse Ising models

TL;DR

This paper introduces an efficient method for estimating sparse high-dimensional Ising models using nonconcave penalized composite likelihood, with theoretical guarantees and practical validation on biological data.

Contribution

It extends nonconcave penalized likelihood methods to composite likelihood for high-dimensional Ising models, enabling efficient estimation with proven asymptotic properties.

Findings

Method achieves accurate sparse structure recovery in simulations.

Application to HIV data aligns with known biological insights.

Computational efficiency enables practical high-dimensional inference.

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.