Understanding Interpretability by generalized distillation in Supervised Classification

The ability to interpret decisions taken by Machine Learning (ML) models is fundamental to encourage trust and reliability in different practical applications. Recent interpretation strategies focus on human understanding of the underlying decision mechanisms of the complex ML models. However, these strategies are restricted by the subjective biases of humans. To dissociate from such human biases, we propose an interpretation-by-distillation formulation that is defined relative to other ML models. We generalize the distillation technique for quantifying interpretability, using an information-theoretic perspective, removing the role of ground-truth from the definition of interpretability. Our work defines the entropy of supervised classification models, providing bounds on the entropy of Piece-Wise Linear Neural Networks (PWLNs), along with the first theoretical bounds on the interpretability of PWLNs. We evaluate our proposed framework on the MNIST, Fashion-MNIST and Stanford40 datasets and demonstrate the applicability of the proposed theoretical framework in different supervised classification scenarios.