Quadratic descriptors and reduction methods in a two-layered model for compound inference

Compound inference models are crucial for discovering novel drugs in bioinformatics and chemo-informatics. These models rely heavily on useful descriptors of chemical compounds that effectively capture important information about the underlying compounds for constructing accurate prediction functions. In this article, we introduce quadratic descriptors, the products of two graph-theoretic descriptors, to enhance the learning performance of a novel two-layered compound inference model. A mixed-integer linear programming formulation is designed to approximate these quadratic descriptors for inferring desired compounds with the two-layered model. Furthermore, we introduce different methods to reduce descriptors, aiming to avoid computational complexity and overfitting issues during the learning process caused by the large number of quadratic descriptors. Experimental results show that for 32 chemical properties of monomers and 10 chemical properties of polymers, the prediction functions constructed by the proposed method achieved high test coefficients of determination. Furthermore, our method inferred chemical compounds in a time ranging from a few seconds to approximately 60 s. These results indicate a strong correlation between the properties of chemical graphs and their quadratic graph-theoretic descriptors.