Multivariate Regression Outperforms Several Robust Architectures of Neural Networks in QSAR Modeling

In the past decade, many authors replaced multivariate regression (MR) by the neural networks (NNs) algorithm because they believed the latter to be superior. To verify this, we have undertaken a comparative investigation of the relationship between biological activities and substituent constants representing physicochemical parameters of the substituent groups of 37 carboquinones and 57 benzodiazepines using MR and NNs. A new method for the selection of descriptors in the best possible MR models is presented. The use of orthogonalization procedure makes the calculation of the statistical parameters (e.g. correlation coefficient, R) for each model much simpler, and the selection of the best MR models is accelerated. Such a procedure is applicable to QSAR modeling even for the selection of the best MR model with six descriptors from a set of 100 descriptors. In case one wants to select, for example, the best 15 out of 100 descriptors, a new procedure is developed for the stepwise selection of descriptors in MR models. Using this procedure, we selected not only one (which was the case in the old stepwise MR procedure) but two, three, or more new descriptors in each subsequent step and added them to descriptors selected up to the previous step. The same data sets were previously investigated by several (mainly robust) NN algorithms which contained a hidden layer (Aoyama, T. et al. J. Med. Chem. 1990, 33, 2583−2590; Peterson, K. L. J. Chem. Inf. Comput. Sci. 1995, 35, 896−904; Tetko, I. V. J. Chem. Inf. Comput. Sci. 1996, 36, 794−803), and the authors have concluded that NNs models are better than MR models. These NNs are mainly robust, i.e., contain a large number of connections, and consequently, there are many parameters (weights) that should be optimized. Since it is well-known that NNs with hidden layers take into account nonlinear operations, for a strict comparison between NNs and MR the initial descriptors set used for obtaining MR models should include also nonlinearities. This was done by enlarging the initial descriptor set by including squares and cross-products of initial descriptors. After that, a systematic comparison between MR and this specific architectures of NNs was carried out on seven QSAR models, and MR models were superior in all studied cases.