A Decision-Theoretic Approach for Model Interpretability in Bayesian Framework

TL;DR

This paper introduces a decision-theoretic method for model interpretability in Bayesian frameworks by optimizing a utility function that balances explanation fidelity and interpretability, demonstrated with real-world data.

Contribution

It proposes a model-agnostic approach that finds interpretable proxy models mimicking complex Bayesian models using a utility function, improving accuracy and stability.

Findings

More accurate models at the same interpretability level compared to prior methods.

The approach is model-agnostic and can be applied with standard optimization tools.

Generated models are more stable across different interpretability methods.

Abstract

A salient approach to interpretable machine learning is to restrict modeling to simple models. In the Bayesian framework, this can be pursued by restricting the model structure and prior to favor interpretable models. Fundamentally, however, interpretability is about users' preferences, not the data generation mechanism; it is more natural to formulate interpretability as a utility function. In this work, we propose an interpretability utility, which explicates the trade-off between explanation fidelity and interpretability in the Bayesian framework. The method consists of two steps. First, a reference model, possibly a black-box Bayesian predictive model which does not compromise accuracy, is fitted to the training data. Second, a proxy model from an interpretable model family that best mimics the predictive behaviour of the reference model is found by optimizing the interpretability utility function. The approach is model agnostic -- neither the interpretable model nor the reference model are restricted to a certain class of models -- and the optimization problem can be solved using standard tools. Through experiments on real-word data sets, using decision trees as interpretable models and Bayesian additive regression models as reference models, we show that for the same level of interpretability, our approach generates more accurate models than the alternative of restricting the prior. We also propose a systematic way to measure stability of interpretabile models constructed by different interpretability approaches and show that our proposed approach generates more stable models.