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.
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Acknowledgments
The authors would like to thank Sabine Müller and Moritz Wolter for helpful discussions and constructive feedback. Parts of this research have been funded by the Federal Ministry of Education and Research of Germany and the state of North-Rhine Westphalia as part of the Lamarr-Institute for Machine Learning and Artificial Intelligence (LAMARR22B), as well as by the Fraunhofer Cluster of Excellence Cognitive Internet Technologies (CCIT) and by the Fraunhofer Research Center Machine Learning (FZML).
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Heese, R., Mücke, S., Jakobs, M., Gerlach, T., Piatkowski, N. (2023). Shapley Values with Uncertain Value Functions. In: Crémilleux, B., Hess, S., Nijssen, S. (eds) Advances in Intelligent Data Analysis XXI. IDA 2023. Lecture Notes in Computer Science, vol 13876. Springer, Cham. https://doi.org/10.1007/978-3-031-30047-9_13
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DOI: https://doi.org/10.1007/978-3-031-30047-9_13
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