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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 byhighlighting open challenges in using interpretable machine learning techniques to make discoveries, including gaps between theory and practice for validating data-driven discoveries. 

Consensus clustering has been widely used in bioinformatics and other applications to improve the accuracy, stability and reliability of clustering results. This approach ensembles cluster co-occurrences from multiple clustering runs on subsampled observations. For application to large-scale bioinformatics data, such as to discover cell types from single-cell sequencing data, for example, consensus clustering has two significant drawbacks: (i) computational inefficiency due to repeatedly applying clustering algorithms, and (ii) lack of interpretability into the important features for differentiating clusters. In this paper, we address these two challenges by developing IMPACC: Interpretable MiniPatch Adaptive Consensus Clustering. Our approach adopts three major innovations. We ensemble cluster co-occurrences from tiny subsets of both observations and features, termed minipatches, thus dramatically reducing computation time. Additionally, we develop adaptive sampling schemes for observations, which result in both improved reliability and computational savings, as well as adaptive sampling schemes of features, which lead to interpretable solutions by quickly learning the most relevant features that differentiate clusters. We study our approach on synthetic data and a variety of real large-scale bioinformatics data sets; results show that our approach not only yields more accurate and interpretable cluster solutions, but it also substantially improves computational efficiency compared to standard consensus clustering approaches.