Interpretable Machine Learning for Discovery: Statistical Challenges \&
  Opportunities
Genevera I. Allen Luqin Gan Lili Zheng
New technologies have led to vast troves of large and complex datasets across
many scientific domains and industries. People routinely use machine learning
techniques to not only process, visualize, and make predictions from this 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 paper, 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
from both 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.