Cited By
View all- Labreuche C(2024)Contribution of Subsets of Variables in Global Sensitivity Analysis with Dependent VariablesScalable Uncertainty Management10.1007/978-3-031-76235-2_18(233-248)Online publication date: 12-Nov-2024
Fast Joint Shapley Values
Pages 285 - 287
Abstract
The Shapley value has recently drawn the attention of the data management community. Briefly, the Shapley value is a well-known numerical measure for the contribution of a player to a coalitional game. In the direct extension of Shapley axioms, the newly introduced joint Shapley value provides a measure for the average contribution of a set of players. However, due to its exponential nature, it is computationally intensive: for an explanation order of k, the original algorithm takes O(min(3^n, 2^n n^k)) time. In this work, we improve it to O(2^n nk).
Supplemental Material
MP4 File
Fast Joint Shapley Values: introduces the reverse Moebius transform to speed-up the Shapley value defined over sets of players.
- Download
- 110.07 MB
References
[1]
Bedoor K. Alshebli, Tomasz P. Michalak, Oskar Skibski, Michael Wooldridge, and Talal Rahwan. 2019. A Measure of Added Value in Groups. ACM Trans. Auton. Adapt. Syst., Vol. 13, 4, Article 18 (jul 2019), 46 pages. https://doi.org/10.1145/3335547
[2]
Andreas Björklund, Thore Husfeldt, Petteri Kaski, and Mikko Koivisto. 2007. Fourier Meets Möbius: Fast Subset Convolution. In Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing (San Diego, California, USA) (STOC '07). Association for Computing Machinery, New York, NY, USA, 67--74. https://doi.org/10.1145/1250790.1250801
[3]
Nicolas Bousquet, Zhentao Li, and Adrian Vetta. 2015. Coalition Games on Interaction Graphs: A Horticultural Perspective. In Proceedings of the Sixteenth ACM Conference on Economics and Computation (Portland, Oregon, USA) (EC '15). Association for Computing Machinery, New York, NY, USA, 95--112. https://doi.org/10.1145/2764468.2764477
[4]
Kedar Dhamdhere, Ashish Agarwal, and Mukund Sundararajan. 2020. The Shapley Taylor Interaction Index. In Proceedings of the 37th International Conference on Machine Learning (ICML'20). JMLR.org, Article 858, 10 pages.
[5]
Michel Grabisch and Marc Roubens. 1999. An axiomatic approach to the concept of interaction among players in cooperative games. International Journal of Game Theory, Vol. 28, 4 (01 Nov 1999), 547--565. https://doi.org/10.1007/s001820050125
[6]
Chris Harris, Richard Pymar, and Colin Rowat. 2021. Joint Shapley values: a measure of joint feature importance. https://doi.org/10.48550/ARXIV.2107.11357
[7]
Robert Kennes and Philippe Smets. 2013. Computational Aspects of the Mobius Transform. ArXiv, Vol. abs/1304.1122 (2013).
[8]
Donald E. Knuth. 2006. The Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees--History of Combinatorial Generation (Art of Computer Programming). Addison-Wesley Professional.
[9]
Ester Livshits, Leopoldo E. Bertossi, Benny Kimelfeld, and Moshe Sebag. 2019. The Shapley Value of Tuples in Query Answering. In International Conference on Database Theory.
[10]
Scott M Lundberg and Su-In Lee. 2017. A Unified Approach to Interpreting Model Predictions. In Advances in Neural Information Processing Systems, I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Eds.), Vol. 30. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2017/file/8a20a8621978632d76c43dfd28b67767-Paper.pdf
[11]
Jean-Luc Marichal, Ivan Kojadinovic, and Katsushige Fujimoto. 2007. Axiomatic characterizations of generalized values. Discrete Applied Mathematics, Vol. 155, 1 (2007), 26--43. https://doi.org/10.1016/j.dam.2006.05.002
[12]
Mihail Stoian. 2022. Fast Joint Shapley Values. https://github.com/stoianmihail/fast-joint-shapley/
[13]
Erik vS trumbelj and Igor Kononenko. 2014. Explaining prediction models and individual predictions with feature contributions. Knowledge and Information Systems, Vol. 41, 3 (01 Dec 2014), 647--665. https://doi.org/10.1007/s10115-013-0679-x io
Index Terms
- Fast Joint Shapley Values
Recommendations
Coalition-weighted Shapley values
AbstractWe introduce a new class of values for coalitional games: the coalition-weighted Shapley values. Weights can be assigned to coalitions, not just to players, and zero-weights are admissible. The Shapley value belongs to this class. Coalition-...
Shapley Values with Uncertain Value Functions
Advances in Intelligent Data Analysis XXIAbstractWe 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-...
On connections between individual values and coalition values for games in characteristic function form
This paper investigates some connections between individual values, such as the Shapley value and the Banzhaf value, and coalition values, such as blockability value, viability value and profitability value, for games in characteristic function form. It ...
Comments
Information & Contributors
Information
Published In
June 2023
330 pages
ISBN:9781450395076
DOI:10.1145/3555041
- General Chairs:
- Sudipto Das,
- Ippokratis Pandis,
- Program Chairs:
- K. Selçuk Candan,
- Sihem Amer-Yahia
Copyright © 2023 Owner/Author.
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 05 June 2023
Check for updates
Author Tags
Qualifiers
- Abstract
Data Availability
Fast Joint Shapley Values: introduces the reverse Moebius transform to speed-up the Shapley value defined over sets of players. https://dl.acm.org/doi/10.1145/3555041.3589393#Shapley-final.mp4
Conference
SIGMOD/PODS '23
Sponsor:
Acceptance Rates
Overall Acceptance Rate 785 of 4,003 submissions, 20%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 145Total Downloads
- Downloads (Last 12 months)51
- Downloads (Last 6 weeks)4
Reflects downloads up to 03 Mar 2025
Other Metrics
Citations
Cited By
View all- Labreuche C(2024)Contribution of Subsets of Variables in Global Sensitivity Analysis with Dependent VariablesScalable Uncertainty Management10.1007/978-3-031-76235-2_18(233-248)Online publication date: 12-Nov-2024
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in