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

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 (ML) 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 ML models and offers insights into the conceptual differences with existing training set selection approaches.