References

Aas, Kjersti, Martin Jullum, and Anders Løland. 2020. “Explaining Individual Predictions When Features Are Dependent: More Accurate Approximations to Shapley Values.” arXiv:1903.10464 [Cs, Stat], February. http://arxiv.org/abs/1903.10464.

Adler, Philip, Casey Falk, Sorelle A. Friedler, Gabriel Rybeck, Carlos Scheidegger, Brandon Smith, and Suresh Venkatasubramanian. 2016. “Auditing Black-Box Models for Indirect Influence.” arXiv:1602.07043 [Cs, Stat], November. http://arxiv.org/abs/1602.07043.

Basu, Debraj. 2020. “On Shapley Credit Allocation for Interpretability.” arXiv:2012.05506 [Cs, Stat], December. http://arxiv.org/abs/2012.05506.

Beckers, Sander. 2022. “Causal Explanations and XAI.” arXiv:2201.13169 [Cs], February. http://arxiv.org/abs/2201.13169.

Castro, Javier, Daniel Gómez, and Juan Tejada. 2009. “Polynomial Calculation of the Shapley Value Based on Sampling.” Computers & Operations Research 36 (5): 1726–30. https://doi.org/10.1016/j.cor.2008.04.004.

Chen, Hugh, Joseph D. Janizek, Scott Lundberg, and Su-In Lee. 2020. “True to the Model or True to the Data?” arXiv:2006.16234 [Cs, Stat], June. http://arxiv.org/abs/2006.16234.

Covert, Ian C. 2020. “Explaining by Removing: A Unified Framework for Model Explanation.” arXiv:2011.14878 [Cs], 90.

Datta, Anupam, Shayak Sen, and Yair Zick. 2016. “Algorithmic Transparency via Quantitative Input Influence: Theory and Experiments with Learning Systems.” In 2016 IEEE Symposium on Security and Privacy (SP), 598–617. https://doi.org/10.1109/SP.2016.42.

Feldman, Barry. 2005. “The Proportional Value of a Cooperative Game,” 30.

Frye, Christopher, Colin Rowat, and Ilya Feige. 2020. “Asymmetric Shapley Values: Incorporating Causal Knowledge into Model-Agnostic Explainability.” arXiv:1910.06358 [Cs, Stat], October. http://arxiv.org/abs/1910.06358.

Grömping, Ulrike. 2007. “Estimators of Relative Importance in Linear Regression Based on Variance Decomposition.” The American Statistician 61 (2): 139–47. https://www.jstor.org/stable/27643865.

Halpern, Joseph Y., and Judea Pearl. 2005a. “Causes and Explanations: A Structural-Model Approach. Part I: Causes.” The British Journal for the Philosophy of Science 56 (4): 843–87. http://www.jstor.org/stable/3541870.

———. 2005b. “Causes and Explanations: A Structural-Model Approach. Part II: Explanations.” The British Journal for the Philosophy of Science 56 (4): 889–911. https://www.jstor.org/stable/3541871.

Heskes, Tom, Evi Sijben, Ioan Gabriel Bucur, and Tom Claassen. 2020. “Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models.” arXiv:2011.01625 [Cs], November. http://arxiv.org/abs/2011.01625.

Janzing, Dominik, Lenon Minorics, and Patrick Blöbaum. 2019. “Feature Relevance Quantification in Explainable AI: A Causal Problem.” arXiv:1910.13413 [Cs, Stat], November. http://arxiv.org/abs/1910.13413.

Kilbertus, Niki, Mateo Rojas-Carulla, Giambattista Parascandolo, Moritz Hardt, Dominik Janzing, and Bernhard Schölkopf. 2018. “Avoiding Discrimination Through Causal Reasoning.” arXiv:1706.02744 [Cs, Stat], January. http://arxiv.org/abs/1706.02744.

Kruskal, William. 1987. “Relative Importance by Averaging Over Orderings.” The American Statistician 41 (1): 6–10. https://doi.org/10.2307/2684310.

Kumar, I. Elizabeth, Suresh Venkatasubramanian, Carlos Scheidegger, and Sorelle Friedler. 2020. “Problems with Shapley-Value-Based Explanations as Feature Importance Measures.” arXiv:2002.11097 [Cs, Stat], June. http://arxiv.org/abs/2002.11097.

Lindeman, Richard, Peter Merrenda, and Ruth Gold. 1980. Introduction to Bivariate and Multivariate Analysis. Glenview, IL.

Lipovetsky, Stan, and Michael Conklin. 2001. “Analysis of Regression in Game Theory Approach.” Applied Stochastic Models in Business and Industry 17 (4): 319–30. https://doi.org/10.1002/asmb.446.

Lundberg, Scott, and Su-In Lee. 2017. “A Unified Approach to Interpreting Model Predictions.” arXiv:1705.07874 [Cs, Stat], November. http://arxiv.org/abs/1705.07874.

Merrick, Luke, and Ankur Taly. 2020. “The Explanation Game: Explaining Machine Learning Models Using Shapley Values.” arXiv:1909.08128 [Cs, Stat], June. http://arxiv.org/abs/1909.08128.

Miller, Tim. 2018. “Explanation in Artificial Intelligence: Insights from the Social Sciences.” arXiv:1706.07269 [Cs], August. http://arxiv.org/abs/1706.07269.

Mittelstadt, Brent, Chris Russell, and Sandra Wachter. 2019. “Explaining Explanations in AI.” Proceedings of the Conference on Fairness, Accountability, and Transparency, January, 279–88. https://doi.org/10.1145/3287560.3287574.

Owen, Art B. 2014. “Sobol’ Indices and Shapley Value.” SIAM/ASA Journal on Uncertainty Quantification 2 (1): 245–51. https://doi.org/10.1137/130936233.

Owen, Art B., and Clémentine Prieur. 2017. “On Shapley Value for Measuring Importance of Dependent Inputs.” SIAM/ASA Journal on Uncertainty Quantification 5 (1): 986–1002. https://doi.org/10.1137/16M1097717.

Pearl, Judea. 2009. Causality: Models, Reasoning, and Inference. Second. Cambridge University Press.

Pearl, Judea, Madelyn Glymour, and Nicholas P. Jewell. 2016. Causal Inference in Statistics: A Primer. Wiley.

Shapley, L. 1953. “A Value for n-Person Games.” In Contributions to the Theory of Games, 2:307–17. Princeton, NJ: Princeton University Press.

Singal, Raghav, George Michailidis, and Hoiyi Ng. 2021. “Flow-Based Attribution in Graphical Models: A Recursive Shapley Approach.” {SSRN} {Scholarly} {Paper} ID 3845526. Rochester, NY: Social Science Research Network. https://doi.org/10.2139/ssrn.3845526.

Song, Eunhye, Barry L. Nelson, and Jeremy Staum. 2016. “Shapley Effects for Global Sensitivity Analysis: Theory and Computation.” SIAM/ASA Journal on Uncertainty Quantification 4 (1): 1060–83. https://doi.org/10.1137/15M1048070.

Strumbelj, Erik, and Igor Kononenko. 2010. “An Efficient Explanation of Individual Classifications Using Game Theory.” The Journal of Machine Learning Research 11 (March): 1–18.

Štrumbelj, E., I. Kononenko, and M. Robnik Šikonja. 2009. “Explaining Instance Classifications with Interactions of Subsets of Feature Values.” Data & Knowledge Engineering 68 (10): 886–904. https://doi.org/10.1016/j.datak.2009.01.004.

Štrumbelj, Erik, and Igor Kononenko. 2014. “Explaining Prediction Models and Individual Predictions with Feature Contributions.” Knowledge and Information Systems 41 (3): 647–65. https://doi.org/10.1007/s10115-013-0679-x.

Stufken, John. 1992. “On Hierarchical Partitioning.” The American Statistician 46 (1): 70–71. http://www.jstor.org/stable/2684415.

Sundararajan, Mukund, and Amir Najmi. 2020. “The Many Shapley Values for Model Explanation.” arXiv:1908.08474 [Cs, Econ], February. http://arxiv.org/abs/1908.08474.

Viswanathan, Vignesh, and Yair Zick. 2021. “Model Explanations via the Axiomatic Causal Lens.” arXiv:2109.03890 [Cs], September. http://arxiv.org/abs/2109.03890.

Wachter, Sandra, Brent Mittelstadt, and Chris Russell. 2018. “Counterfactual Explanations Without Opening the Black Box: Automated Decisions and the GDPR.” arXiv:1711.00399 [Cs], March. http://arxiv.org/abs/1711.00399.

Wang, Jiaxuan, Jenna Wiens, and Scott Lundberg. 2021. “Shapley Flow: A Graph-Based Approach to Interpreting Model Predictions.” arXiv:2010.14592 [Cs, Stat], February. http://arxiv.org/abs/2010.14592.

Zhao, Qingyuan, and Trevor Hastie. 2021. “Causal Interpretations of Black-Box Models.” Journal of Business & Economic Statistics 39 (1): 272–81. https://doi.org/10.1080/07350015.2019.1624293.