High-dimensional generalized linear models incorporating graphical structure among predictors

Abstract

In this paper, we propose a sparse generalized linear model incorporating graphical structure among predictors (sGLMg), which is an extension of [37] where they exploit the structure information among predictors to improve the performance for the linear regression. There is an explicit expression between the coefficient and the predictor graph measured by the precision matrix in the linear regression, however, this structure does not exist in generalized linear model for the explicit expression of the coefficient in generalized linear model is usually hard to be obtained. To incorporate the graphical structure among predictors for generalized linear models, we make use of the sufficient reduction techniques to reestablish the relationship between the coefficient and the precision matrix. The oracle inequalities of the estimator for sGLMg are also presented and the finite sample performance of the proposed methods is examined via numerical simulations and a breast cancer data analysis.