Kernel Banzhaf: A Fast and Robust Estimator for Banzhaf Values

2024-10-10

arXiv.org

AI Summary

This paper addresses the inefficiency of Monte Carlo sampling in estimating the Banzhaf value—a computationally attractive alternative to the Shapley value. We propose Kernel Banzhaf, the first method that formulates Banzhaf value estimation as a regression problem. Its key contributions are: (1) establishing a rigorous equivalence between the regression objective and the true Banzhaf value; (2) designing a kernelized solution framework with theoretical convergence guarantees that avoids combinatorial explosion; and (3) leveraging the kernel trick to efficiently handle subset sampling. Evaluated on eight benchmark datasets, Kernel Banzhaf significantly outperforms existing Monte Carlo approaches—achieving superior accuracy, sample efficiency, noise robustness, and fidelity in feature ranking recovery. The method is theoretically grounded in both robustness and interpretability, offering a principled, scalable, and practical alternative for efficient attribution estimation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Banzhaf values provide a popular, interpretable alternative to the widely-used Shapley values for quantifying the importance of features in machine learning models. Like Shapley values, computing Banzhaf values exactly requires time exponential in the number of features, necessitating the use of efficient estimators. Existing estimators, however, are limited to Monte Carlo sampling methods. In this work, we introduce Kernel Banzhaf, the first regression-based estimator for Banzhaf values. Our approach leverages a novel regression formulation, whose exact solution corresponds to the exact Banzhaf values. Inspired by the success of Kernel SHAP for Shapley values, Kernel Banzhaf efficiently solves a sampled instance of this regression problem. Through empirical evaluations across eight datasets, we find that Kernel Banzhaf significantly outperforms existing Monte Carlo methods in terms of accuracy, sample efficiency, robustness to noise, and feature ranking recovery. Finally, we complement our experimental evaluation with strong theoretical guarantees on Kernel Banzhaf's performance.

Problem

• Introduces Kernel Banzhaf for Banzhaf values
• Improves accuracy and efficiency over Monte Carlo
• Provides theoretical guarantees on performance

Innovation

• Regression-based Banzhaf estimator
• Novel regression formulation
• Efficient solution for feature importance