  Black box models in machine learning have demonstrated excellent predictive
performance in complex problems and high-dimensional settings. However, their
lack of transparency and interpretability restrict the applicability of such
models in critical decision-making processes. In order to combat this
shortcoming, we propose a novel approach to trading off interpretability and
performance in prediction models using ideas from semiparametric statistics,
allowing us to combine the interpretability of parametric regression models
with performance of nonparametric methods. We achieve this by utilizing a
two-piece model: the first piece is interpretable and parametric, to which a
second, uninterpretable residual piece is added. The performance of the overall
model is optimized using methods from the sufficient dimension reduction
literature. Influence function based estimators are derived and shown to be
doubly robust. This allows for use of approaches such as double Machine
Learning in estimating our model parameters. We illustrate the utility of our
approach via simulation studies and a data application based on predicting the
length of stay in the intensive care unit among surgery patients.
