Learning Hybrid Interpretable Models: Theory, Taxonomy, and Methods

TL;DR

This paper provides a comprehensive analysis of hybrid interpretable models, exploring their theoretical foundations, taxonomy, and new methods, demonstrating their potential to outperform black boxes while maintaining transparency.

Contribution

It introduces a unified framework for understanding, classifying, and implementing hybrid models, including the novel HybridCORELS method that offers optimality guarantees and transparency control.

Findings

Hybrid models can outperform standalone black boxes in certain settings.

HybridCORELS achieves competitive performance with enhanced interpretability.

Theoretical PAC guarantees identify an optimal transparency trade-off.

Abstract

A hybrid model involves the cooperation of an interpretable model and a complex black box. At inference, any input of the hybrid model is assigned to either its interpretable or complex component based on a gating mechanism. The advantages of such models over classical ones are two-fold: 1) They grant users precise control over the level of transparency of the system and 2) They can potentially perform better than a standalone black box since redirecting some of the inputs to an interpretable model implicitly acts as regularization. Still, despite their high potential, hybrid models remain under-studied in the interpretability/explainability literature. In this paper, we remedy this fact by presenting a thorough investigation of such models from three perspectives: Theory, Taxonomy, and Methods. First, we explore the theory behind the generalization of hybrid models from the Probably-Approximately-Correct (PAC) perspective. A consequence of our PAC guarantee is the existence of a sweet spot for the optimal transparency of the system. When such a sweet spot is attained, a hybrid model can potentially perform better than a standalone black box. Secondly, we provide a general taxonomy for the different ways of training hybrid models: the Post-Black-Box and Pre-Black-Box paradigms. These approaches differ in the order in which the interpretable and complex components are trained. We show where the state-of-the-art hybrid models Hybrid-Rule-Set and Companion-Rule-List fall in this taxonomy. Thirdly, we implement the two paradigms in a single method: HybridCORELS, which extends the CORELS algorithm to hybrid modeling. By leveraging CORELS, HybridCORELS provides a certificate of optimality of its interpretable component and precise control over transparency. We finally show empirically that HybridCORELS is competitive with existing hybrid models, and performs just as well as a standalone black box (or even better) while being partly transparent.