Proxy-Based Approximation of Shapley and Banzhaf Interactions

TL;DR

ProxySHAP introduces a novel, efficient method for accurately approximating Shapley and Banzhaf interactions in machine learning models, outperforming previous estimators in speed and accuracy.

Contribution

It provides a polynomial-time generalization for exact interaction computation in tree ensembles and analyzes residual correction strategies for bias reduction.

Findings

ProxySHAP achieves state-of-the-art approximation accuracy.

It outperforms ProxySPEX and KernelSHAP-IQ in large-scale applications.

ProxySHAP delivers superior downstream explainability performance.

Abstract

Shapley and Banzhaf interactions capture the complex dynamics inherent in modern machine learning applications. However, current estimators for these higher-order interactions trade off between speed and accuracy. To overcome this limitation, we introduce ProxySHAP. ProxySHAP reconciles the high sample efficiency of tree-based proxy models with a principled path to consistency via residual correction. On a theoretical level, we derive a polynomial-time generalization of interventional TreeSHAP to compute exact interaction indices for tree ensembles, successfully bypassing exponential tree-depth dependencies in prior methods. Furthermore, we formally analyze the residual adjustment strategy, characterizing the specific conditions under which Maximum Sample Reuse (MSR) corrects proxy bias without its variance scaling exponentially with interaction size. Extensive benchmarking demonstrates that ProxySHAP sets a new state-of-the-art standard for approximation quality, including in large-scale applications with thousands of features. By achieving the lowest error in both small- and large-budget regimes, ProxySHAP significantly outperforms the prior best estimators ProxySPEX and KernelSHAP-IQ, while also delivering superior performance on downstream explainability tasks.