  Deep models have advanced prediction in many domains, but their lack of
interpretability remains a key barrier to the adoption in many real world
applications. There exists a large body of work aiming to help humans
understand these black box functions to varying levels of granularity -- for
example, through distillation, gradients, or adversarial examples. These
methods however, all tackle interpretability as a separate process after
training. In this work, we take a different approach and explicitly regularize
deep models so that they are well-approximated by processes that humans can
step-through in little time. Specifically, we train several families of deep
neural networks to resemble compact, axis-aligned decision trees without
significant compromises in accuracy. The resulting axis-aligned decision
functions uniquely make tree regularized models easy for humans to interpret.
Moreover, for situations in which a single, global tree is a poor estimator, we
introduce a regional tree regularizer that encourages the deep model to
resemble a compact, axis-aligned decision tree in predefined,
human-interpretable contexts. Using intuitive toy examples as well as medical
tasks for patients in critical care and with HIV, we demonstrate that this new
family of tree regularizers yield models that are easier for humans to simulate
than simpler L1 or L2 penalties without sacrificing predictive power.
