Identifying Nonlinear Relationships in Regression using the ACE Algorithm

Gasoline quality prediction using the alternating conditional expectation (ACE) algorithm and ATR-FTIR

Accurate estimation of oxygenates is a critical issue in the quality evaluation of gasoline samples. This work aims to examine the nonparametric robust principal component analysis-alternating conditional expectation (rPCA-ACE) algorithm combined with FTIR spectroscopy as a rapid and accurate analytical method for predicting the quality of gasoline samples based on oxygenates content (methanol, methyl tert-butyl ether, and isobutanol). In the ACE algorithm, a set of optimal transformations is estimated for both the independent and dependent variables. These transformations reveal their non-linear relationships and generate a maximum linear effect between the transformed independent variables and the transformed response variable. In this study, the ACE algorithm was applied to an empirical gasoline dataset and considered a series of possible transformations of the independent and dependent variables to find the best transformations. Among all possible transformations, the ACE algorithm identified a series of polynomials and a nearly linear transformation as the best transformations for the independent and dependent variables, respectively. The regression statistics for calibration and prediction, including the correlation coefficient (Rcal2 = 0.9692), root mean square error of calibration (RMSEC = 2.8638), and root mean square error of prediction (RMSEP = 4.0498) (%v/v) for oxygenates content, were calculated. The ACE model showed improved regression results compared to the linear PLS model (Rcal2 = 0.9550, RMSEC = 3.9052, RMSEP = 5.1342) and PCR model (Rcal2 = 0.9160, RMSEC = 6.5330, RMSEP = 7.0270). By applying the ACE technique to the synthetic fully non-linear dataset obtained from the equation y'=exp(y) for the response variable, we demonstrated the power of the ACE algorithm in multivariate analysis and its ability to identify the exact functional relationship between independent and dependent variables to solve fully non-linear problems.

RKappa: Software for Analyzing Rule-Based Models

RKappa is a framework for the development, simulation, and analysis of rule-based models within the mature statistically empowered R environment. It is designed for model editing, parameter identification, simulation, sensitivity analysis, and visualization. The framework is optimized for high-performance computing platforms and facilitates analysis of large-scale systems biology models where knowledge of exact mechanisms is limited and parameter values are uncertain.The RKappa software is an open-source (GLP3 license) package for R, which is freely available online ( https://github.com/lptolik/R4Kappa ).

Data-based identifiability analysis of non-linear dynamical models

MOTIVATION

Mathematical modelling of biological systems is becoming a standard approach to investigate complex dynamic, non-linear interaction mechanisms in cellular processes. However, models may comprise non-identifiable parameters which cannot be unambiguously determined. Non-identifiability manifests itself in functionally related parameters, which are difficult to detect.

RESULTS

We present the method of mean optimal transformations, a non-parametric bootstrap-based algorithm for identifiability testing, capable of identifying linear and non-linear relations of arbitrarily many parameters, regardless of model size or complexity. This is performed with use of optimal transformations, estimated using the alternating conditional expectation algorithm (ACE). An initial guess or prior knowledge concerning the underlying relation of the parameters is not required. Independent, and hence identifiable parameters are determined as well. The quality of data at disposal is included in our approach, i.e. the non-linear model is fitted to data and estimated parameter values are investigated with respect to functional relations. We exemplify our approach on a realistic dynamical model and demonstrate that the variability of estimated parameter values decreases from 81 to 1% after detection and fixation of structural non-identifiabilities.