The Shapley Value of Classifiers in Ensemble Games

TL;DR

This paper introduces ensemble games and a scalable algorithm called Troupe for estimating the Shapley value of classifiers, providing a new way to evaluate and select models in ensemble learning.

Contribution

The paper proposes a novel framework of ensemble games and an efficient algorithm for approximating Shapley values, aiding model importance assessment and ensemble pruning.

Findings

Shapley values effectively identify important models in ensembles.

Troupe algorithm provides accurate, scalable Shapley value estimates.

Using Shapley values improves ensemble performance and robustness.

Abstract

What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles, pre-trained models cooperate to make classification decisions. To quantify the importance of models in these ensemble games, we define \textit{Troupe} -- an efficient algorithm which allocates payoffs based on approximate Shapley values of the classifiers. We argue that the Shapley value of models in these games is an effective decision metric for choosing a high performing subset of models from the ensemble. Our analytical findings prove that our Shapley value estimation scheme is precise and scalable; its performance increases with size of the dataset and ensemble. Empirical results on real world graph classification tasks demonstrate that our algorithm produces high quality estimates of the Shapley value. We find that Shapley values can be utilized for ensemble pruning, and that adversarial models receive a low valuation. Complex classifiers are frequently found to be responsible for both correct and incorrect classification decisions.