Jianshen Zhu ¹ Naveed Ahmed Azam ^2* Shengjuan Cao ¹ Ryota Ido ¹ Kazuya Haraguchi ¹ Liang Zhao ³ Hiroshi Nagamochi ¹ Tatsuya Akutsu ⁴

• ¹ Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Kyōto, Japan
• ² Department of Mathematics, Faculty of Natural Sciences, Quaid-i-Azam University, Islamabad, Islamabad, Pakistan
• ³ Graduate School of Advanced Integrated Studies in Human Survavibility (Shishu-Kan), Kyoto University, Kyoto, Japan, Kyoto, Japan
• ⁴ Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Japan

Compound inference models are crucial for discovering novel drugs in bioinformatics and chemoinformatics. 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 paper, 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 ten 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 range from a few seconds to around 60 seconds. These results indicate a strong correlation between the properties of chemical graphs and their quadratic graph-theoretic descriptors.