We present a brief history of the field of interpretable machine learning (IML), give an overview of state-of-the-art interpretation methods, and discuss challenges. Research in IML has boomed in recent years. As young as the field is, it has over 200 years old roots in regression modeling and rule-based machine learning, starting in the 1960s. Recently, many new IML methods have been proposed, many of them model-agnostic, but also interpretation techniques specific to deep learning and tree-based ensembles. IML methods either directly analyze model components, study sensitivity to input perturbations, or analyze local or global surrogate approximations of the ML model. The field approaches a state of readiness and stability, with many methods not only proposed in research, but also implemented in open-source software. But many important challenges remain for IML, such as dealing with dependent features, causal interpretation, and uncertainty estimation, which need to be resolved for its successful application to scientific problems. A further challenge is a missing rigorous definition of interpretability, which is accepted by the community. To address the challenges and advance the field, we urge to recall our roots of interpretable, data-driven modeling in statistics and (rule-based) ML, but also to consider other areas such as sensitivity analysis, causal inference, and the social sciences.
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