Networks Based on Regression Models and Prediction Methods

Abstract

Prediction methods (e.g., linear and nonlinear regression models) can be used to construct a network among a set of vectors x ₁, …, x _n . The construction follows three steps. First, the prediction method is used to predict y = x _j on the basis of x = x _i . Second, a measure of predictive accuracy or statistical significance (e.g., a likelihood ratio test p value) is calculated. Third, the measure is transformed into an adjacency measure A _ij between the two vectors. Although general prediction and machine learning methods can be used, we focus on regression models for measuring nonlinear relationships (e.g., polynomial and spline regression models). Spline regression models are attractive since they provide a statistical framework for robustly capturing general nonlinear relationships. Generalized linear models allow one to model the relationship between binary variables, count data, and categorical variables. Multivariate regression models allow one to define a pairwise adjacency measure between variables, which conditions on additional covariates, which describe sample properties (e.g., batch effects). The partial correlation coefficient can be interpreted as a pairwise correlation measure which adjusts for other variables. Partial correlation networks can be used to define networks that encode direct relationships between variables.