Interpretable machine learning has become a strong competitor for traditional black-box models. However, the possible loss of the predictive performance for gaining interpretability is often inevitable, putting practitioners in a dilemma of choosing between high accuracy (black-box models) and interpretability (interpretable models). In this work, we propose a novel framework for building a Hybrid Predictive Model (HPM) that integrates an interpretable model with any black-box model to combine their strengths. The interpretable model substitutes the black-box model on a subset of data where the black-box is overkill or nearly overkill, gaining transparency at no or low cost of the predictive accuracy. We design a principled objective function that considers predictive accuracy, model interpretability, and model transparency (defined as the percentage of data processed by the interpretable substitute.) Under this framework, we propose two hybrid models, one substituting with association rules and the other with linear models, and we design customized training algorithms for both models. We test the hybrid models on structured data and text data where interpretable models collaborate with various state-of-the-art black-box models. Results show that hybrid models obtain an efficient trade-off between transparency and predictive performance, characterized by our proposed efficient frontiers.
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