# An Inverse QSAR Method Based on Linear Regression and Integer Programming

arXiv: https://arxiv.org/abs/2107.02381 · HTML: https://mlsanity.com/paper/2107.02381/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 6 Jul 2021.

## Builds on (most cited first, 9 of 9)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [GraphNVP: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/1905.11600/) (2019)
- [ChemTS: An Efficient Python Library for de novo Molecular Generation](https://mlsanity.com/paper/1710.00616/) (2017)
- [A Novel Method for Inference of Acyclic Chemical Compounds with Bounded Branch-height Based on Artificial Neural Networks and Integer Programming](https://mlsanity.com/paper/2009.09646/) (2020)
- [A novel method for inference of chemical compounds with prescribed topological substructures based on integer programming](https://mlsanity.com/paper/2010.09203/) (2020)

## Built on by (most cited first, 3 of 3)

- [Combining Graph Neural Networks and Mixed Integer Linear Programming for Molecular Inference under the Two-Layered Model](https://mlsanity.com/paper/2507.03920/) (2025)
- [Cycle-Configuration: A Novel Graph-theoretic Descriptor Set for Molecular Inference](https://mlsanity.com/paper/2408.05136/) (2024)
- [Mixing Vector Model for Copolymer Inference via Mixed Integer Linear Programming](https://mlsanity.com/paper/2605.29329/) (2026)

## Abstract (arXiv)

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 η(x) of a chemical property π to C. After this, we formulate an MILP that simulates the computation process of f(C) from C and that of η(x) from x. Given a target value y^* of the chemical property π, we infer a chemical graph C^dagger such that η(f(C^dagger))=y^* by solving the MILP. In this paper, we use linear regression to construct a prediction function η 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.