  Driven by an increasing need for model interpretability, interpretable models
have become strong competitors for black-box models in many real applications.
In this paper, we propose a novel type of model where interpretable models
compete and collaborate with black-box models. We present the Model-Agnostic
Linear Competitors (MALC) for partially interpretable classification. MALC is a
hybrid model that uses linear models to locally substitute any black-box model,
capturing subspaces that are most likely to be in a class while leaving the
rest of the data to the black-box. MALC brings together the interpretable power
of linear models and good predictive performance of a black-box model. We
formulate the training of a MALC model as a convex optimization. The predictive
accuracy and transparency (defined as the percentage of data captured by the
linear models) balance through a carefully designed objective function and the
optimization problem is solved with the accelerated proximal gradient method.
Experiments show that MALC can effectively trade prediction accuracy for
transparency and provide an efficient frontier that spans the entire spectrum
of transparency.
