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Deep neural networks (DNN) have been demonstrated to achieve unparalleled prediction accuracy in a wide range of applications. Despite its strong performance, in certain areas, the usage of DNN has met resistance because of its black-box nature. In this article, we propose a new method to estimate a mixture of linear models (MLM) for regression or classification that is relatively easy to interpret. We use DNN as a proxy of the optimal prediction function such that MLM can be effectively estimated. We propose visualization methods and quantitative approaches to interpret the predictor by MLM. Experiments show that the new method allows us to tradeoff interpretability and accuracy. The MLM estimated under the guidance of a trained DNN fills the gap between a highly explainable linear statistical model and a highly accurate but difficult to interpret predictor.  Supplementary materials  for this article are available online.

Mixture of Linear Models Co-supervised by Deep Neural Networks