Shapley Values with Uncertain Value Functions

TL;DR

This paper introduces a new way to compute Shapley values when the value functions are uncertain, such as in non-deterministic machine learning models, by using probability theory to handle randomness.

Contribution

It defines Shapley values for uncertain value functions from first principles and shows how to incorporate randomness into the calculation, extending the applicability of Shapley values.

Findings

Uncertain value functions can be modeled with probability theory.

Random effects can be absorbed into shifted noiseless value functions.

Evaluating these Shapley values reliably requires more computation.

Abstract

We propose a novel definition of Shapley values with uncertain value functions based on first principles using probability theory. Such uncertain value functions can arise in the context of explainable machine learning as a result of non-deterministic algorithms. We show that random effects can in fact be absorbed into a Shapley value with a noiseless but shifted value function. Hence, Shapley values with uncertain value functions can be used in analogy to regular Shapley values. However, their reliable evaluation typically requires more computational effort.