Beyond Shapley: Efficient Computation of Asymmetric Shapley Values

2026-06-23

AI Summary

This work addresses the computational intractability of standard SHAP due to its #P-hard complexity in feature attribution by integrating causal knowledge into the interpretability framework. The authors propose Asymmetric Shapley Values (ASV) grounded in causal graphs, leveraging equivalence classes derived from topological orderings of the causal structure. They establish, for the first time, a polynomial-time exact algorithm for computing ASV under rooted directed tree structures and further develop an efficient approximation algorithm applicable to arbitrary causal directed acyclic graphs (DAGs). Experimental results demonstrate that the proposed approach substantially improves computational efficiency on real-world causal structures while preserving high-quality explanation fidelity.

Abstract

We address the problem of explainability in machine learning models through feature attribution methods. In particular, we consider a variant of Shapley values known as Asymmetric Shapley Values (ASV), which enables the incorporation of causal knowledge into model-agnostic explanations through the use of a causal graph. We show that in certain contexts in which the computation of SHAP is $\#P$-hard, the exact computation of ASV can be done in polynomial time. To extend this algorithmic result, we introduce a notion of equivalence classes over the topological orderings of the underlying causal graph, which is useful to reduce the time to compute ASV. In particular, we present a polynomial-time algorithm (in the number of equivalence classes) to compute it whenever the causal graph is a rooted directed tree. Finally, we develop an algorithm for approximating ASV in arbitrary causal DAGs which relies on a procedure to sample topological orderings uniformly at random. To implement this sampling mechanism we leverage known algorithms as well as simpler alternatives. Our experimental results demonstrate the practical viability of the proposed approach in realistic causal structures.

Problem

• Asymmetric Shapley Values
• feature attribution
• causal graph
• model interpretability
• computational complexity

Innovation

• Asymmetric Shapley Values
• causal graph
• polynomial-time algorithm
• topological ordering
• feature attribution