Nonlinear Multivariate Polynomial Ensembles in QSAR/QSPR

摘要

In this study, which is part of Damir Nadramija's PhD thesis developed in collaboration with The Rudjer BoSkovic Institute, we demonstrate use of ensembles of linear and nonlinear multivariate regression models, based on multivariate polynomials of initial descriptors, in QSAR/QSPR modeling. Data sets, which varied significantly in size regarding number of variables and number of points, were all previously referenced in literature and molecular structures were either obtained from authorsof these publications or generated in our laboratories. All data sets were encoded as SMILES and converted to 3D structures (SD files) by the CORINA program (www2.chemie.uni-erlangen.de/software/corina/). All descriptors were computed by the program DRAGON 2.1 (http://www.disat.unimib.it/chm/). Linear ensembles were built with multiple linear regression models (MLR) and nonlinear ensembles consisted of multivariate polynomials, which were constructed as controlled subsets selected among linear descriptors, their two-fold cross-products and squares, as well as cubic potencies of (only) single descriptors. Ensemble responses were computed as mean or median or weighted values of all intrinsic models. Models and ensembles discussed in this paper were constructed with the application NQSAR, a Windows console application, which is available upon request. Results obtained show clear advantage of nonlinear ensembles over linear counterparts when data sets contain 4 to 5 times more points than model coefficients. On the other side linear ensembles, which in general exhibit higher robustness and stability, are better suited for small data sets with many variables outperforming nonlinear ensembles in predicting values of data points from external data set. This can be explained by the fact that the linear models are less affected by small variations than nonlinear models while they equally benefit from the key ensemble features. Primarily, we note the impact of the inclusion of more variables spread across optimized variable subsets, which are used in ensembles' intrinsic models that individually satisfy before mentioned rule on over-fitting. The overall ensemble responses are more stable and robust with higher predictive powers than single models.