Abstract
Inverse-QSPR is a method to propose chemical structures having desired properties by inversely analyzing regression models. In general, QSPR models are neither surjective nor injective, so it is difficult to define the pre-image of these models. The authors once proposed to solve this problem by using probability distribution. In that method, Bayesian theorem played a crucial role to retrieve posterior distribution of independent variables given an objective variable value. Although that method works well for some case studies, regression models must be constructed using Multiple Linear Regression (MLR). This premise, however, does not fit many cases. To overcome this limitation, herewith we have developed two methodologies for inverse-QSPR. One is using different MLR models for each cluster, defined by Gaussian mixture models. The other is using Gaussian mixture regression. Both of them can analytically define the posterior probability distribution of independent variables for inverse analysis. We investigated how both of them capture features of data with nonlinearity and showed they worked well at least for a simulation dataset.
