Learning Interpretable Models Using an Oracle

We look at a specific aspect of model interpretability: 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 an oracle, a highly accurate probabilistic model on the training data. The uncertainty in the oracle's predictions are used to learn a sampling distribution for the training data. The interpretable model is then trained on a data sample obtained using this distribution, leading often to significantly greater accuracy. We formulate the sampling strategy as an optimization problem. Our solution1 possesses the following key favorable properties: (1) it uses a fixed number of seven optimization variables, irrespective of the dimensionality of the data (2) it is model agnostic - in that both the interpretable model and the oracle may belong to arbitrary model families (3) it has a flexible notion of model size, and can accommodate vector sizes (4) it is a framework, enabling it to benefit from progress in the area of optimization. We also present the following interesting observations: (a) In general, the optimal training distribution at small model sizes is different from the test distribution; (b) This effect exists even when the interpretable model and the oracle are from highly disparate model families: we show this on a text classification task, by using a Gated Recurrent Unit network as an oracle to improve the sequence classification accuracy of a Decision Tree that uses character n-grams; (c) Our technique may be used to identify an optimal training sample of a given sample size, for a model.