nach oben

Erschienen in:

2023 | OriginalPaper | Buchkapitel

Shapley Values with Uncertain Value Functions

verfasst von : Raoul Heese, Sascha Mücke, Matthias Jakobs, Thore Gerlach, Nico Piatkowski

Erschienen in: Advances in Intelligent Data Analysis XXI

Verlag: Springer Nature Switzerland

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Effects of Locality and Rule Language on Explanations for Knowledge Graph Embeddings

Nächstes Kapitel Revised Conditional t-SNE: Looking Beyond the Nearest Neighbors

Watson, D.S.: Interpretable machine learning for genomics. Hum. Genet. 141(9), 1499–1513 (2022)CrossRef

Amann, J., Blasimme, A., Vayena, E., Frey, D., Madai, V.I., Precise4Q Consortium.: Explainability for artificial intelligence in healthcare: a multidisciplinary perspective. BMC Med. Inform. Decis. Making, 20(1), 310 (2020)

Zhong, X., Gallagher, B., Liu, S., Kailkhura, B., Hiszpanski, A., Han, T.Y.J.: Explainable machine learning in materials science. NPJ Comput. Mater. 8(1), 204 (2022)CrossRef

Carta, S., Podda, A.S., Reforgiato Recupero, D., Stanciu, M.M.: Explainable AI for financial forecasting. In: Nicosia, G., et al. (eds.) LOD 2021. LNCS, vol. 13164, pp. 51–69. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-95470-3_5CrossRef

Molnar, C.: Interpretable Machine Learning 2 ed (2022). github.io

Shapley, L.S.: A value for n-person games. Contrib. Theory Games 2(28), 307–317 (1953)MathSciNetMATH

Grömping, U.: Estimators of relative importance in linear regression based on variance decomposition. Am. Stat. 61(2), 139–147 (2007)MathSciNetCrossRef

Štrumbelj, E., Kononenko, I.: An efficient explanation of individual classifications using game theory. J. Mach. Learn. Res. 11, 1–18 (2010)MathSciNetMATH

Štrumbelj, E., Kononenko, I.: Explaining prediction models and individual predictions with feature contributions. Knowl. Inf. Syst. 41(3), 647–665 (2014)CrossRef

10.

Lundberg, S.M., Lee, S.I.: A unified approach to interpreting model predictions. In: Advances in Neural Information Processing Systems (2017)

11.

Merrick, L., Taly, A.: The explanation game: explaining machine learning models using Shapley values. In: Holzinger, A., Kieseberg, P., Tjoa, A.M., Weippl, E. (eds.) CD-MAKE 2020. LNCS, vol. 12279, pp. 17–38. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57321-8_2CrossRef

12.

Sundararajan, M., Najmi, A.: The many Shapley values for model explanation. In: Daumé III, H., Singh, A.,(eds.) International Conference on Machine Learning of Proceedings of Machine Learning Research, vol. 119, pp. 9269–9278. PMLR (2020)

13.

Belle, V., Papantonis, I.: Principles and practice of explainable machine learning. Front. Big Data 4, 39 (2021)CrossRef

14.

Rozemberczki, B., Watson, L., Bayer, P., Yang, H.T., Kiss, O., Nilsson, S., Sarkar, R.: The shapley value in machine learning. Olivér Kiss (2022)

15.

Štrumbelj, E., Kononenko, I., Robnik Šikonja, M.: Explaining instance classifications with interactions of subsets of feature values. Data Knowl. Eng. 68(10), 886–904 (2009)CrossRef

16.

Li, X., Zhou, Y., Dvornek, N.C., Gu, Y., Ventola, P., Duncan, J.S.: Efficient Shapley explanation for features importance estimation under uncertainty. In: Martel, A.L., et al. (eds.) MICCAI 2020. LNCS, vol. 12261, pp. 792–801. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59710-8_77CrossRef

17.

Shrikumar, A., Greenside, P., Kundaje, A.: Learning important features through propagating activation differences. In: International Conference on Machine Learning, Proceedings of Machine Learning Research, pp. 3145–3153. JMLR.org (2017)

18.

Kargin, V.: Uncertainty of the Shapley value. Int. Game Theory Rev. 07(04), 517–529 (2005)MathSciNetCrossRefMATH

19.

Fatima, S.S., Wooldridge, M., Jennings, N.R.: An analysis of the Shapley value and its uncertainty for the voting game. In: La Poutré, H., Sadeh, N.M., Janson, S. (eds.) AMEC/TADA -2005. LNCS (LNAI), vol. 3937, pp. 85–98. Springer, Heidelberg (2006). https://doi.org/10.1007/11888727_7CrossRef

20.

Gao, J., Yang, X., Liu, D.: Uncertain Shapley value of coalitional game with application to supply chain alliance. Appl. Soft Comput. 56, 551–556 (2017)CrossRef

21.

Dai, B., Yang, X., Liu, X.: Shapley value of uncertain coalitional game based on Hurwicz criterion with application to water resource allocation. Group Decis. Negot. 31(1), 241–260 (2022)CrossRef

22.

Yang, X., Gao, J.: Uncertain differential games with application to capitalism. J. Uncertainty Anal. Appl. 1(1), 17 (2013)CrossRef

23.

Liu, B.: Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty, vol. 300. Springer, Heidelberg (2010)

24.

Hart, S.: Game Theory, chapter Shapley Value, pp. 210–216. Palgrave Macmillan UK, London (1989)

25.

Aumann, R.J., Shapley, L.S.: Values of Non-Atomic Games. Princeton University Press, New Jersey (1974)MATH

26.

Dubey, P.: On the uniqueness of the Shapley value. Internet. J. Game Theory 4, 131–139 (1975)MathSciNetCrossRefMATH

27.

Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15(56), 1929–1958 (2014)MathSciNetMATH

28.

Deng, X., Papadimitriou, C.H.: On the complexity of cooperative solution concepts. Math. Oper. Res. 19(2), 257–266 (1994)MathSciNetCrossRefMATH

29.

Aas, K., Jullum, M., Løland, A.: Explaining individual predictions when features are dependent: more accurate approximations to Shapley values. Artif. Intell. 298, 103502 (2021)MathSciNetCrossRefMATH

30.

Touati, S., Radjef, M.S., Sais, L.: A Bayesian Monte Carlo method for computing the Shapley value: application to weighted voting and bin packing games. Comput. Oper. Res. 125, 105094 (2021)MathSciNetCrossRefMATH

31.

Mitchell, R., Cooper, J., Frank, E., Holmes, G.: Sampling permutations for Shapley value estimation (2021)

32.

Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)MathSciNetMATH

33.

Lundberg, S.M., et al.: From local explanations to global understanding with explainable AI for trees. Nat. Mach. Intell. 2(1), 56–67 (2020)CrossRef

34.

López, S., Saboya, M.: On the relationship between Shapley and Owen values. Cent. Eur. J. Oper. Res. 17(4), 415 (2009)MathSciNetCrossRefMATH

35.

Saavedra-Nieves, A., Fiestras-Janeiro, M.G.: Sampling methods to estimate the Banzhaf-Owen value. Ann. Oper. Res. 301(1), 199–223 (2021)MathSciNetCrossRefMATH

36.

Cerezo, M., Verdon, G., Huang, H.Y., Cincio, L., Coles, P.J.: Challenges and opportunities in quantum machine learning. Nat. Comput. Sci. 2(9), 567–576 (2022)CrossRef

Titel: Shapley Values with Uncertain Value Functions
verfasst von: Raoul Heese
Sascha Mücke
Matthias Jakobs
Thore Gerlach
Nico Piatkowski
Verlag: Springer Nature Switzerland
Buch: Advances in Intelligent Data Analysis XXI
Print ISBN: 978-3-031-30046-2

Electronic ISBN: 978-3-031-30047-9

Copyright-Jahr: 2023
DOI: https://doi.org/10.1007/978-3-031-30047-9_13

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner