Shapley Values as a Strategy for Ensemble Weights Estimation

Abstract

This study introduces a novel performance-based weighting scheme for ensemble learning using the Shapley value. The weighting uses the reciprocal of binary cross-entropy as a base learner’s performance metric and estimates its Shapley value to measure the overall contribution of a learner to an equally weighted ensemble of various sizes. Two variants of this strategy were empirically compared with a single monolith model and other static weighting strategies using two large banking-related datasets. A variant that discards learners with a negative Shapley value was ranked as first or at least second when constructing homogeneous ensembles, whereas for heterogeneous ensembles this strategy resulted in a better or at least similar detection performance to other weighting strategies tested. The main limitation being the computational complexity of Shapley calculations, the explored weighting strategy could be considered as a generalization of performance-based weighting.

Keywords

• machine learning
• ensemble methods
• Shapley value
• performance weighting
• privacy-preserving distributed learning