An Inverse QSAR Method Based on Linear Regression and Integer Programming

• URL: http://arxiv.org/abs/2107.02381v1
• Date: Tue, 6 Jul 2021 04:37:55 GMT
• Title: An Inverse QSAR Method Based on Linear Regression and Integer Programming
• Authors: Jianshen Zhu, Naveed Ahmed Azam, Kazuya Haraguchi, Liang Zhao, Hiroshi Nagamochi and Tatsuya Akutsu
• Abstract summary: We propose a framework for designing the molecular structure of chemical compounds using both artificial neural networks (ANNs) and mixed integer linear programming (MILP) In this paper, we use linear regression to construct a prediction function $eta$ instead of ANNs. The results of computational experiments suggest our method can infer chemical graphs with around up to 50 non-hydrogen atoms.
• Score: 6.519339570726759
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $f(C)$ of a chemical graph $C$ and construct an ANN that maps $x=f(C)$ to a predicted value $\eta(x)$ of a chemical property $\pi$ to $C$. After this, we formulate an MILP that simulates the computation process of $f(C)$ from $C$ and that of $\eta(x)$ from $x$. Given a target value $y^*$ of the chemical property $\pi$, we infer a chemical graph $C^\dagger$ such that $\eta(f(C^\dagger))=y^*$ by solving the MILP. In this paper, we use linear regression to construct a prediction function $\eta$ instead of ANNs. For this, we derive an MILP formulation that simulates the computation process of a prediction function by linear regression. The results of computational experiments suggest our method can infer chemical graphs with around up to 50 non-hydrogen atoms.

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