Interpretable Machine Learning for Discovery: Statistical Challenges and Opportunities

New technologies have led to vast troves of large and complex data sets across many scientific domains and industries. People routinely use machine learning techniques not only to process, visualize, and make predictions from these big data, but also to make data-driven discoveries. These discoveries are often made using interpretable machine learning, or machine learning models and techniques that yield human-understandable insights. In this article, we discuss and review the field of interpretable machine learning, focusing especially on the techniques, as they are often employed to generate new knowledge or make discoveries from large data sets.We outline the types of discoveries that can be made using interpretable machine learning in both supervised and unsupervised settings. Additionally, we focus on the grand challenge of how to validate these discoveries in a data-driven manner, which promotes trust in machine learning systems and reproducibility in science.We discuss validation both from a practical perspective, reviewing approaches based on data-splitting and stability, as well as from a theoretical perspective, reviewing statistical results on model selection consistency and uncertainty quantification via statistical inference. Finally, we conclude by highlighting open challenges in using interpretable machine learning techniques to make discoveries, including gaps between theory and practice for validating data-driven discoveries.