Learning Interpretable Models Using an Oracle

As Machine Learning (ML) becomes pervasive in various real world systems, the need for models to be understandable has increased. We focus on interpretability, noting that models often need to be constrained in size for them to be considered interpretable, e.g., a decision tree of depth 5 is easier to interpret than one of depth 50. But smaller models also tend to have high bias. This suggests a trade-off between interpretability and accuracy. We propose a model agnostic technique to minimize this trade-off. Our strategy is to first learn a powerful, possibly black-box, probabilistic model -- referred to as the oracle -- on the training data. Uncertainty in the oracle's predictions are used to learn a sampling distribution for the training data. The interpretable model is trained on a sample obtained using this distribution. We demonstrate that such a model often is significantly more accurate than one trained on the original data. Determining the sampling strategy is formulated as an optimization problem. Our solution to this problem possesses the following key favorable properties: (1) the number of optimization variables is independent of the dimensionality of the data: a fixed number of seven variables are used (2) our technique is model agnostic - in that both the interpretable model and the oracle may belong to arbitrary model families. Results using multiple real world datasets, using Linear Probability Models and Decision Trees as interpretable models, with Gradient Boosted Model and Random Forest as oracles, are presented. We observe significant relative improvements in the F1-score in most cases, occasionally seeing improvements greater than 100%. Additionally, we discuss an interesting application of our technique where a Gated Recurrent Unit network is used to improve the sequence classification accuracy of a Decision Tree that uses character n-grams as features.