Analyzing complex mathematical model behavior by partial least squares regression‐based multivariate metamodeling

Abstract

The increasing complexity of mathematical models of complex systems like living cells has created a need for methods to reduce computational demand, maintain overview of the capabilities and feasibility of the models, compare alternative models, and obtain more reliable and effective fitting of models to experimental data. Metamodeling—statistical modeling of the behavior of complex mathematical models, also called ‘surrogate modeling’—is well established in many scientific disciplines, such as mechanical engineering and process simulation, and has recently also found use in computational biology, as well as other fields of bioscience. Many of these are based on partial least squares regression (PLSR) and various nonlinear and N‐way extensions of the PLSR. This is a versatile family of multivariate data modeling methods that combines a simple, flexible model structure (low‐rank bilinear subspace regression) and an intuitively attractive optimization criterion (maximized explained input–output covariance) to provide both predictive ability and graphical insight. This review summarizes the background for PLSR‐based metamodeling, and the use of PLSR and related methods in the main application areas of metamodeling: reduction of computational demand, sensitivity analysis, model comparison, and parameterization of models in relation to measured data. The methodology is generic, but here illustrated by examples from computational biology. The advantages and limitations of metamodeling for analyzing complex model behavior are discussed. WIREs Comput Stat 2014, 6:440–475. doi: 10.1002/wics.1325This article is categorized under: Applications of Computational Statistics > Computational and Molecular Biology Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods