Machine Learning in Discrete Molecular Spaces

The past decade has seen an explosion of machine learning in chemistry. Whether it is in property prediction, synthesis, molecular design, or any other subdivision, machine learning seems poised to become an integral, if not a dominant, component of future research efforts. This extraordinary capacity rests on the interac- tion between machine learning models and the underlying chemical data landscape commonly referred to as chemical space. Chemical space has multiple incarnations, but is generally considered the space of all possible molecules. In this sense, it is one example of a molecular set: an arbitrary collection of molecules. This thesis is devoted to precisely these objects, and particularly how they interact with machine learning models. This work is predicated on the idea that by better understanding the relationship between molecular sets and the models trained on them we can improve models, achieve greater interpretability, and further break down the walls between data-driven and human-centric chemistry. The hope is that this enables the full predictive power of machine learning to be leveraged while continuing to build our understanding of chemistry. The first three chapters of this thesis introduce and reviews the necessary machine learning theory, particularly the tools that have been specially designed for chemical problems. This is followed by an extensive literature review in which the contributions of machine learning to multiple facets of chemistry over the last two decades are explored. Chapters 4-7 explore the research conducted throughout this PhD. Here we explore how we can meaningfully describe the properties of an arbitrary set of molecules through information theory; how we can determine the most informative data points in a set of molecules; how graph signal processing can be used to understand the relationship between the chosen molecular representation, the property, and the machine learning model; and finally how this approach can be brought to bear on protein space. Each of these sub-projects briefly explores the necessary mathematical theory before leveraging it to provide approaches that resolve the posed problems. We conclude with a summary of the contributions of this work and outline fruitful avenues for further exploration