# Molecular Design Based on Integer Programming and Splitting Data Sets by Hyperplanes

arXiv: https://arxiv.org/abs/2305.00801 · HTML: https://mlsanity.com/paper/2305.00801/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 52 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 11 of 11)

- [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)
- [Molecular Design Based on Artificial Neural Networks, Integer Programming and Grid Neighbor Search](https://mlsanity.com/paper/2108.10266/) (2021)
- [A Method for Inferring Polymers Based on Linear Regression and Integer Programming](https://mlsanity.com/paper/2109.02628/) (2021)
- [Molecular Design Based on Integer Programming and Quadratic Descriptors in a Two-layered Model](https://mlsanity.com/paper/2209.13527/) (2022)

## Built on by (most cited first, 1 of 1)

- [Combining Graph Neural Networks and Mixed Integer Linear Programming for Molecular Inference under the Two-Layered Model](https://mlsanity.com/paper/2507.03920/) (2025)

## Abstract (arXiv)

A novel framework for designing the molecular structure of chemical compounds with a desired chemical property has recently been proposed. The framework infers a desired chemical graph by solving a mixed integer linear program (MILP) that simulates the computation process of a feature function defined by a two-layered model on chemical graphs and a prediction function constructed by a machine learning method. To improve the learning performance of prediction functions in the framework, we design a method that splits a given data set C into two subsets C(i),i=1,2 by a hyperplane in a chemical space so that most compounds in the first (resp., second) subset have observed values lower (resp., higher) than a threshold θ. We construct a prediction function psi to the data set C by combining prediction functions psii,i=1,2 each of which is constructed on C(i) independently. The results of our computational experiments suggest that the proposed method improved the learning performance for several chemical properties to which a good prediction function has been difficult to construct.