On Shapley value for measuring importance of dependent inputs

TL;DR

This paper advocates for using Shapley value to measure the importance of dependent input variables in functions, highlighting its conceptual advantages over ANOVA-based methods through simple illustrative examples.

Contribution

It demonstrates that Shapley value effectively addresses conceptual issues faced by ANOVA decomposition when inputs are dependent.

Findings

Shapley value provides intuitive importance measures for dependent inputs.

Simple examples show near-closed form solutions using Shapley value.

Shapley value overcomes conceptual limitations of ANOVA-based importance measures.

Abstract

This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables are dependent. Our main goal here is to show that Shapley value removes the conceptual problems. We do this with some simple examples where Shapley value leads to intuitively reasonable nearly closed form values.