On the Computational Tractability of the (Many) Shapley Values

TL;DR

This paper explores the computational complexity of various SHAP value variants across different models and distributions, identifying cases of polynomial-time computability and intractability, thus highlighting the nuanced landscape of SHAP explanations.

Contribution

It extends the analysis of SHAP value computation complexity to multiple variants, models, and distributions, providing new polynomial-time algorithms and intractability results.

Findings

Polynomial-time computation of Interventional and Baseline SHAP under Hidden Markov Model distributions.

Intractability results for neural networks and tree ensembles across several SHAP variants.

Demonstrates the complexity of SHAP values depends on the variant, model, and data distribution.

Abstract

Recent studies have examined the computational complexity of computing Shapley additive explanations (also known as SHAP) across various models and distributions, revealing their tractability or intractability in different settings. However, these studies primarily focused on a specific variant called Conditional SHAP, though many other variants exist and address different limitations. In this work, we analyze the complexity of computing a much broader range of such variants, including Conditional, Interventional, and Baseline SHAP, while exploring both local and global computations. We show that both local and global Interventional and Baseline SHAP can be computed in polynomial time for various ML models under Hidden Markov Model distributions, extending popular algorithms such as TreeSHAP beyond empirical distributions. On the downside, we prove intractability results for these variants over a wide range of neural networks and tree ensembles. We believe that our results emphasize the intricate diversity of computing Shapley values, demonstrating how their complexity is substantially shaped by both the specific SHAP variant, the model type, and the distribution.