When is the Computation of a Feature Attribution Method Tractable?

TL;DR

This paper investigates the computational complexity of feature attribution methods based on power indices, identifying conditions for efficient computation and introducing Bernoulli power indices with simplified calculations.

Contribution

It establishes a simple condition for polynomial-time computation of power indices and introduces Bernoulli power indices with reduced computational complexity.

Findings

Power indices can be computed efficiently under specific conditions.

Bernoulli power indices allow constant expected value evaluations.

Interaction power indices have similar complexity to individual feature indices.

Abstract

Feature attribution methods have become essential for explaining machine learning models. Many popular approaches, such as SHAP and Banzhaf values, are grounded in power indices from cooperative game theory, which measure the contribution of features to model predictions. This work studies the computational complexity of power indices beyond SHAP, addressing the conditions under which they can be computed efficiently. We identify a simple condition on power indices that ensures that computation is polynomially equivalent to evaluating expected values, extending known results for SHAP. We also introduce Bernoulli power indices, showing that their computation can be simplified to a constant number of expected value evaluations. Furthermore, we explore interaction power indices that quantify the importance of feature subsets, proving that their computation complexity mirrors that of individual features.