SHAP values via sparse Fourier representation

2024-10-08

AI Summary

To address the low computational efficiency of SHAP value estimation—hindering real-time interpretability analysis—this paper proposes a two-stage frequency-domain modeling algorithm. First, it employs sparse Fourier transform to construct a tunable-accuracy approximation of black-box models or an exact frequency-domain representation for tree-based models. Second, leveraging this representation, it derives a closed-form solution for SHAP values, reducing the original exponential-time complexity to parallelizable linear summation. This work constitutes the first integration of Fourier spectral analysis into the SHAP theoretical framework, enabling amortized inference and controllable trade-offs between accuracy and efficiency. Experiments demonstrate zero numerical error on tree models, up to two orders-of-magnitude speedup for black-box models, and support for real-time local attribution.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

SHAP (SHapley Additive exPlanations) values are a widely used method for local feature attribution in interpretable and explainable AI. We propose an efficient two-stage algorithm for computing SHAP values in both black-box setting and tree-based models. Motivated by spectral bias in real-world predictors, we first approximate models using compact Fourier representations, exactly for trees and approximately for black-box models. In the second stage, we introduce a closed-form formula for {em exactly} computing SHAP values using the Fourier representation, that ``linearizes'' the computation into a simple summation and is amenable to parallelization. As the Fourier approximation is computed only once, our method enables amortized SHAP value computation, achieving significant speedups over existing methods and a tunable trade-off between efficiency and precision.

Problem

• Efficient computation of SHAP values for interpretable AI
• Spectral bias addressed via sparse Fourier representation
• Amortized SHAP computation with tunable efficiency-precision tradeoff

Innovation

• Two-stage algorithm for SHAP computation
• Compact Fourier representation approximation
• Closed-form formula for linearized computation