Loop-based conic multivariate adaptive regression splines is a novel method for advanced construction of complex biological networks

Abstract

The Gaussian Graphical Model (GGM) and its Bayesian alternative, called, the Gaussian copula graphical model (GCGM) are two widely used approaches to construct the undirected networks of biological systems. They define the interactions between species by using the conditional dependencies of the multivariate normality assumption. However, when the system’s dimension is high, the performance of the model becomes computationally demanding, and, particularly, the accuracy of GGM decreases when the observations are far from normality. Here, we suggest a Conic Multivariate Adaptive Regression Splines (CMARS) as an alternative to GGM and GCGM to ameliorate both problems. CMARS is a modified version of the Multivariate Adaptive Regression Spline, a well-known modeling approaches used in Operational Research (OR) to represent biological, environmental, and economic data. The main benefit of this model is its compatibility with high-dimensional and correlated measurements of serious nonlinearity, which allows for a wide field of application. We adapted CMARS to describe biological systems and called it “LCMARS” due to its loop-based description. We then applied LCMARS to simulated and real datasets, and LCMARS produced more accurate results compared to GGM and GCGM. Hereby, the ability to use LCMARS in the description of biological networks has the potential to open up new avenues in the application of OR to computational biology and bioinformatics, and can thus help us better understanding complex diseases like cancer and hepatitis.