{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T23:05:02Z","timestamp":1778540702608,"version":"3.51.4"},"publisher-location":"Cham","reference-count":30,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031637964","type":"print"},{"value":"9783031637971","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-63797-1_25","type":"book-chapter","created":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T23:03:55Z","timestamp":1720566235000},"page":"489-512","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["How Much Can Stratification Improve the\u00a0Approximation of\u00a0Shapley Values?"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7807-8460","authenticated-orcid":false,"given":"Patrick","family":"Kolpaczki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8904-4904","authenticated-orcid":false,"given":"Georg","family":"Haselbeck","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9944-4108","authenticated-orcid":false,"given":"Eyke","family":"H\u00fcllermeier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,10]]},"reference":[{"key":"25_CR1","unstructured":"European commission. Ethics guidelines for trustworthy AI (2019). https:\/\/ec.europa.eu\/digital-single-market\/en\/news\/ethics-guidelines-trustworthy-ai"},{"key":"25_CR2","unstructured":"Ancona, M., \u00d6ztireli, C., Gross, M.H.: Explaining deep neural networks with a polynomial time algorithm for shapley value approximation. In: Proceedings of International Conference on Machine Learning (ICML), pp. 272\u2013281 (2019)"},{"key":"25_CR3","series-title":"NATO ASI Serie","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/978-94-017-1656-7_12","volume-title":"Game-Theoretic Methods in General Equilibrium Analysis","author":"RJJ Aumann","year":"1994","unstructured":"Aumann, R.J.J.: Economic applications of the shapley value. In: Mertens, J.F., Sorin, S. (eds.) Game-Theoretic Methods in General Equilibrium Analysis. NATO ASI Serie, vol. 77, pp. 121\u2013133. Springer, Dordrecht (1994). https:\/\/doi.org\/10.1007\/978-94-017-1656-7_12"},{"key":"25_CR4","doi-asserted-by":"crossref","unstructured":"Burgess, M.A., Chapman, A.C.: Approximating the shapley value using stratified empirical bernstein sampling. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 73\u201381 (2021)","DOI":"10.24963\/ijcai.2021\/11"},{"key":"25_CR5","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/j.cor.2017.01.019","volume":"82","author":"J Castro","year":"2017","unstructured":"Castro, J., G\u00f3mez, D., Molina, E., Tejada, J.: Improving polynomial estimation of the shapley value by stratified random sampling with optimum allocation. Comput. Oper. Res. 82, 180\u2013188 (2017)","journal-title":"Comput. Oper. Res."},{"issue":"5","key":"25_CR6","doi-asserted-by":"publisher","first-page":"1726","DOI":"10.1016\/j.cor.2008.04.004","volume":"36","author":"J Castro","year":"2009","unstructured":"Castro, J., G\u00f3mez, D., Tejada, J.: Polynomial calculation of the shapley value based on sampling. Comput. Oper. Res. 36(5), 1726\u20131730 (2009)","journal-title":"Comput. Oper. Res."},{"key":"25_CR7","unstructured":"Covert, I., Lundberg, S., Lee, S.I.: Shapley feature utility. In: Machine Learning in Computational Biology (2019)"},{"key":"25_CR8","unstructured":"Covert, I., Lundberg, S.M., Lee, S.: Understanding global feature contributions with additive importance measures. In: Proceedings of Advances in Neural Information Processing Systems (NeurIPS) (2020)"},{"key":"25_CR9","doi-asserted-by":"crossref","unstructured":"Deng, J., Dong, W., Socher, R., Li, L., Li, K., Fei-Fei, L.: Imagenet: a large-scale hierarchical image database. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 248\u2013255 (2009)","DOI":"10.1109\/CVPR.2009.5206848"},{"issue":"2","key":"25_CR10","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1287\/moor.19.2.257","volume":"19","author":"X Deng","year":"1994","unstructured":"Deng, X., Papadimitriou, C.H.: On the complexity of cooperative solution concepts. Math. Oper. Res. 19(2), 257\u2013266 (1994)","journal-title":"Math. Oper. Res."},{"key":"25_CR11","doi-asserted-by":"publisher","unstructured":"Fanaee-T, H.: Bike Sharing. UCI Machine Learning Repository (2013) https:\/\/doi.org\/10.24432\/C5W894","DOI":"10.24432\/C5W894"},{"key":"25_CR12","unstructured":"Ghorbani, A., Zou, J.Y.: Data shapley: equitable valuation of data for machine learning. In: Proceedings of International Conference on Machine Learning (ICML), pp. 2242\u20132251 (2019)"},{"key":"25_CR13","unstructured":"Ghorbani, A., Zou, J.Y.: Neuron shapley: discovering the responsible neurons. In: Proceedings of Advances in Neural Information Processing Systems (NeurIPS) (2020)"},{"key":"25_CR14","doi-asserted-by":"publisher","unstructured":"Hofmann, H.: Statlog (German Credit Data). UCI Machine Learning Repository (1994). https:\/\/doi.org\/10.24432\/C5NC77","DOI":"10.24432\/C5NC77"},{"key":"25_CR15","unstructured":"Ill\u00e9s, F., Ker\u00e9nyi, P.: Estimation of the shapley value by ergodic sampling. CoRR abs\/1906.05224 (2019)"},{"key":"25_CR16","unstructured":"Jia, R., et al.: Towards efficient data valuation based on the shapley value. In: Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS), pp. 1167\u20131176 (2019)"},{"key":"25_CR17","unstructured":"Kohavi, R.: Scaling up the accuracy of Naive-Bayes classifiers: a decision-tree hybrid. In: Proceedings of International Conference on Knowledge Discovery and Data Mining (KDD), pp. 202\u2013207 (1996)"},{"key":"25_CR18","doi-asserted-by":"crossref","unstructured":"Kolpaczki, P., Bengs, V., Muschalik, M., H\u00fcllermeier, E.: Approximating the shapley value without marginal contributions. In: Proceeedings of AAAI Conference on Artificial Intelligence (AAAI), pp. 13246\u201313255 (2024)","DOI":"10.1609\/aaai.v38i12.29225"},{"key":"25_CR19","unstructured":"Lundberg, S.M., Erion, G.G., Lee, S.: Consistent individualized feature attribution for tree ensembles. CoRR abs\/1802.03888 (2018)"},{"key":"25_CR20","unstructured":"Lundberg, S.M., Lee, S.I.: A unified approach to interpreting model predictions. In: Proceedings of Advances in Neural Information Processing Systems (NeurIPS), pp. 4768\u20134777 (2017)"},{"key":"25_CR21","unstructured":"Maleki, S., Tran-Thanh, L., Hines, G., Rahwan, T., Rogers, A.: Bounding the estimation error of sampling-based shapley value approximation with\/without stratifying. CoRR abs\/1306.4265 (2013)"},{"issue":"43","key":"25_CR22","first-page":"1","volume":"23","author":"R Mitchell","year":"2022","unstructured":"Mitchell, R., Cooper, J., Frank, E., Holmes, G.: Sampling permutations for shapley value estimation. J. Mach. Learn. Res. 23(43), 1\u201346 (2022)","journal-title":"J. Mach. Learn. Res."},{"key":"25_CR23","unstructured":"Moro, S., Laureano, R., Cortez, P.: Using data mining for bank direct marketing: an application of the CRIDP-DM methodology. In: Proceedings of European Simulation and Modelling Conference (ESM) (2011)"},{"issue":"4","key":"25_CR24","doi-asserted-by":"publisher","first-page":"558","DOI":"10.2307\/2342192","volume":"97","author":"J Neyman","year":"1934","unstructured":"Neyman, J.: On the two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. J. Roy. Stat. Soc. 97(4), 558\u2013625 (1934)","journal-title":"J. Roy. Stat. Soc."},{"issue":"6","key":"25_CR25","doi-asserted-by":"publisher","first-page":"2837","DOI":"10.1109\/TSG.2015.2402194","volume":"6","author":"G O\u2019Brien","year":"2015","unstructured":"O\u2019Brien, G., Gamal, A.E., Rajagopal, R.: Shapley value estimation for compensation of participants in demand response programs. IEEE Trans. Smart Grid 6(6), 2837\u20132844 (2015)","journal-title":"IEEE Trans. Smart Grid"},{"key":"25_CR26","doi-asserted-by":"crossref","unstructured":"Okhrati, R., Lipani, A.: A multilinear sampling algorithm to estimate shapley values. In: Proceedings of International Conference on Pattern Recognition (ICPR), pp. 7992\u20137999 (2020)","DOI":"10.1109\/ICPR48806.2021.9412511"},{"key":"25_CR27","doi-asserted-by":"crossref","unstructured":"Rozemberczki, B., Sarkar, R.: The shapley value of classifiers in ensemble games. In: Proceedings of ACM International Conference on Information and Knowledge Management (CIKM), pp. 1558\u20131567 (2021)","DOI":"10.1145\/3459637.3482302"},{"key":"25_CR28","doi-asserted-by":"crossref","unstructured":"Rozemberczki, B., et al.: The shapley value in machine learning. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 5572\u20135579 (2022)","DOI":"10.24963\/ijcai.2022\/778"},{"key":"25_CR29","doi-asserted-by":"crossref","unstructured":"Shapley, L.S.: A value for n-person games. In: Contributions to the Theory of Games (AM-28), Volume II, pp. 307\u2013318. Princeton University Press (1953)","DOI":"10.1515\/9781400881970-018"},{"issue":"3","key":"25_CR30","first-page":"1","volume":"8","author":"T van Campen","year":"2018","unstructured":"van Campen, T., Hamers, H., Husslage, B., Lindelauf, R.: A new approximation method for the shapley value applied to the WTC 9\/11 terrorist attack. Soc. Netw. Anal. Min. 8(3), 1\u201312 (2018)","journal-title":"Soc. Netw. Anal. Min."}],"container-title":["Communications in Computer and Information Science","Explainable Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-63797-1_25","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,23]],"date-time":"2024-11-23T19:20:49Z","timestamp":1732389649000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-63797-1_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031637964","9783031637971"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-63797-1_25","relation":{},"ISSN":["1865-0929","1865-0937"],"issn-type":[{"value":"1865-0929","type":"print"},{"value":"1865-0937","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"10 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"xAI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"World Conference on Explainable Artificial Intelligence","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Valletta","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Malta","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"xai2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/xaiworldconference.com\/2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}