An Inverse QSAR Method Based on Decision Tree and Integer Programming

Abstract

Recently a novel framework has been proposed for designing the molecular structure of chemical compounds using both artificial neural networks (ANNs) and mixed integer linear programming (MILP). In the framework, we first define a feature vector f(${\mathbb{C}}$) of a chemical graph ${\mathbb{C}}$ and construct an ANN that maps x = f(${\mathbb{C}}$) to a predicted value η(x) of a chemical property π to ${\mathbb{C}}$. After this, we formulate an MILP that simulates the computation process of f(${\mathbb{C}}$) from ${\mathbb{C}}$ and that of η(x) from x. Given a target value y^∗ of the chemical property π, we infer a chemical graph ${\mathbb{C}}$^† such that η(f(${\mathbb{C}}$^†)) = y^∗ by solving the MILP. In this paper, in pursuit of alternative learning models, we design an original decision tree that is based on a set of separating hyperplanes in the feature space which is then used to construct a prediction function η instead of ANNs. For this, we derive an MILP formulation that simulates the computation process of the proposed decision tree. The results of computational experiments suggest our method can infer chemical graphs with around up to 50 non-hydrogen atoms and that the prediction function based on a decision tree outperforms that with ANNs for several chemical properties.