Integer linear programming for unsupervised training set selection in molecular machine learning

TL;DR

This paper introduces an integer linear programming method for selecting molecular training sets in physics-inspired machine learning, improving prediction accuracy for larger molecules by optimizing local similarity-based selection.

Contribution

The paper presents a novel ILP-based algorithm for unsupervised training set selection that outperforms existing methods, especially for larger molecules.

Findings

Outperforms existing training set selection methods.

Improves predictions for molecules larger than training set molecules.

Efficiently finds optimal solutions using ILP.

Abstract

Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we demonstrate the relevance of an ILP formulation to select molecular training sets for predictions of size-extensive properties. We show that our algorithm outperforms existing unsupervised training set selection approaches, especially when predicting properties of molecules larger than those present in the training set. We argue that the reason for the improved performance is due to the selection that is based on the notion of local similarity (i.e., per-atom) and a unique ILP approach that finds optimal solutions efficiently. Altogether, this work provides a practical algorithm to improve the performance of physics-inspired machine learning models and offers insights into the conceptual differences with existing training set selection approaches.