An Inverse QSAR Method Based on Linear Regression and Integer Programming

TL;DR

This paper introduces an inverse QSAR method that uses linear regression and integer programming to design chemical structures with desired properties, simplifying the process compared to neural network approaches.

Contribution

The paper presents a novel inverse QSAR framework combining linear regression with MILP, enabling chemical graph inference for property optimization.

Findings

Can infer chemical graphs with up to 50 non-hydrogen atoms.

Demonstrates effectiveness of linear regression-based inverse QSAR.

Provides MILP formulation for linear regression prediction functions.

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.