Shapley Values with Uncertain Value Functions
This work addresses a specific issue in explainable AI for researchers and practitioners dealing with non-deterministic models, but it is incremental as it extends existing Shapley value theory rather than introducing a new paradigm.
The paper tackles the problem of computing Shapley values when value functions are uncertain, such as in non-deterministic machine learning algorithms, by proposing a novel definition based on probability theory. It shows that random effects can be absorbed into a shifted noiseless value function, allowing uncertain Shapley values to be used similarly to regular ones, though with increased computational effort.
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.