{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T05:05:36Z","timestamp":1790053536339,"version":"4.0.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T00:00:00Z","timestamp":1720396800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T00:00:00Z","timestamp":1720396800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Lucy Family Institute for Data and Society, University of Notre Dame"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>With the rise of artificial intelligence in our everyday lives, the need for human interpretation of machine learning models\u2019 predictions emerges as a critical issue. Generally, interpretability is viewed as a binary notion with a performance trade-off. Either a model is fully-interpretable but lacks the ability to capture more complex patterns in the data, or it is a black box. In this paper, we argue that this view is severely limiting and that instead interpretability should be viewed as a continuous domain-informed concept. We leverage the well-known Mixture of Experts architecture with user-defined limits on non-interpretability. We extend this idea with a counterfactual fairness module to ensure the selection of consistently <jats:italic>fair<\/jats:italic> experts: <jats:bold>FairMOE<\/jats:bold>. We perform an extensive experimental evaluation with fairness-related data sets and compare our proposal against state-of-the-art methods. Our results demonstrate that FairMOE is competitive with the leading fairness-aware algorithms in both fairness and predictive measures while providing more consistent performance, competitive scalability, and, most importantly, greater interpretability.<\/jats:p>","DOI":"10.1007\/s10994-024-06583-2","type":"journal-article","created":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T22:01:39Z","timestamp":1720476099000},"page":"6539-6559","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["FairMOE: counterfactually-fair mixture of experts with levels of interpretability"],"prefix":"10.1007","volume":"113","author":[{"given":"Joe","family":"Germino","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nuno","family":"Moniz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nitesh V.","family":"Chawla","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,8]]},"reference":[{"issue":"1","key":"6583_CR1","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/s10115-017-1116-3","volume":"54","author":"P Adler","year":"2018","unstructured":"Adler, P., Falk, C., Friedler, S. A., Nix, T., Rybeck, G., Scheidegger, C., Smith, B., & Venkatasubramanian, S. (2018). Auditing black-box models for indirect influence. Knowledge and Information Systems, 54(1), 95\u2013122.","journal-title":"Knowledge and Information Systems"},{"key":"6583_CR2","unstructured":"Agarwal, A., Beygelzimer, A., Dud \u00edk, M., Langford, J., & Wallach, H. (2018). A reductions approach to fair classification. In International conference on machine learning (pp. 60\u201369). PMLR."},{"key":"6583_CR3","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.inffus.2019.12.012","volume":"58","author":"AB Arrieta","year":"2020","unstructured":"Arrieta, A. B., D\u00edaz-Rodr\u00edguez, N., Del Ser, J., Bennetot, A., Tabik, S., Barbado, A., Garc\u00eda, S., Gil-L\u00f3pez, S., Molina, D., & Benjamins, R. (2020). Explainable artificial intelligence (xai): Concepts, taxonomies, opportunities and challenges toward responsible ai. Information Fusion, 58, 82\u2013115.","journal-title":"Information Fusion"},{"key":"6583_CR4","doi-asserted-by":"crossref","unstructured":"Balagopalan, A., Zhang, H., Hamidieh, K., Hartvigsen, T., Rudzicz, F., & Ghassemi, M. (2022). The road to explainability is paved with bias: Measuring the fairness of explanations. In Proceedings of the 2022 ACM conference on fairness, accountability, and transparency (pp. 1194\u20131206).","DOI":"10.1145\/3531146.3533179"},{"key":"6583_CR5","unstructured":"Bird, S., Dud\u00edk, M., Edgar, R., Horn, B., Lutz, R., Milan, V., Sameki, M., Wallach, H., & Walker, K. (2020). Fairlearn: A toolkit for assessing and improving fairness in AI. Microsoft, Tech. Rep. MSR-TR-2020-32."},{"issue":"8","key":"6583_CR6","doi-asserted-by":"publisher","first-page":"832","DOI":"10.3390\/electronics8080832","volume":"8","author":"DV Carvalho","year":"2019","unstructured":"Carvalho, D. V., Pereira, E. M., & Cardoso, J. S. (2019). Machine learning interpretability: A survey on methods and metrics. Electronics, 8(8), 832.","journal-title":"Electronics"},{"key":"6583_CR7","doi-asserted-by":"publisher","unstructured":"Census-Income (KDD). (2000). UCI machine learning repository. https:\/\/doi.org\/10.24432\/C5N30T .","DOI":"10.24432\/C5N30T"},{"key":"6583_CR8","volume-title":"Integrated public use microdata series international","author":"MP Center","year":"2013","unstructured":"Center, M. P. (2013). Integrated public use microdata series international. University of Minnesota Minneapolis."},{"key":"6583_CR9","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1007\/978-3-319-71246-8_29","volume-title":"Machine learning and knowledge discovery in databases","author":"V Cerqueira","year":"2017","unstructured":"Cerqueira, V., Torgo, L., Pinto, F., & Soares, C. (2017). Arbitrated ensemble for time series forecasting. In M. Ceci, J. Hollm\u00e9n, L. Todorovski, C. Vens, & S. D\u017eeroski (Eds.), Machine learning and knowledge discovery in databases (pp. 478\u2013494). Cham: Springer."},{"key":"6583_CR10","doi-asserted-by":"crossref","unstructured":"Chakraborty, J., Majumder, S., & Menzies, T. (2021). Bias in machine learning software: Why? How? What to do? In Proceedings of the 29th ACM joint meeting on European software engineering conference and symposium on the foundations of software engineering (pp. 429\u2013440).","DOI":"10.1145\/3468264.3468537"},{"issue":"01","key":"6583_CR11","first-page":"9","volume":"4","author":"B Chandrasekaran","year":"1989","unstructured":"Chandrasekaran, B., Tanner, M. C., & Josephson, J. R. (1989). Explaining control strategies in problem solving. IEEE Intelligent Systems, 4(01), 9\u201315.","journal-title":"IEEE Intelligent Systems"},{"key":"6583_CR12","unstructured":"Cynthia, D., Moritz, H., Toniann, P., Omer, R., & Richard, Z. (2012). Fairness through awareness. In Proceedings of the 3rd innovations in theoretical computer science conference (pp. 214\u2013226). Association for Computing Machinery, New York, NY, USA."},{"key":"6583_CR13","first-page":"361","volume":"70","author":"KR Davis","year":"2004","unstructured":"Davis, K. R. (2004). Age discrimination and disparate impact-a new look at an age-old problem. Brook. L. Rev., 70, 361.","journal-title":"Brook. L. Rev."},{"key":"6583_CR14","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1016\/j.future.2022.01.026","volume":"131","author":"H Ding","year":"2022","unstructured":"Ding, H., Chen, L., Dong, L., Fu, Z., & Cui, X. (2022). Imbalanced data classification: A knn and generative adversarial networks-based hybrid approach for intrusion detection. Future Generation Computer Systems, 131, 240\u2013254.","journal-title":"Future Generation Computer Systems"},{"key":"6583_CR15","unstructured":"Doshi-Velez, F., & Kim, B. (2017). Towards a rigorous science of interpretable machine learning. arXiv preprint arXiv:1702.08608."},{"key":"6583_CR16","unstructured":"Dua, D., & Graff, C. (2017). UCI machine learning repository. http:\/\/archive.ics.uci.edu\/ml."},{"key":"6583_CR17","unstructured":"Frost, N., Lipton, Z., Mansour, Y., & Moshkovitz, M. (2024). Partially interpretable models with guarantees on coverage and accuracy. In International conference on algorithmic learning theory (pp. 590\u2013613). PMLR."},{"key":"6583_CR18","doi-asserted-by":"crossref","unstructured":"Garg, S., Perot, V., Limtiaco, N., Taly, A., Chi, E. H., & Beutel, A. (2019). Counterfactual fairness in text classification through robustness. In Proceedings of the 2019 AAAI\/ACM conference on AI, ethics, and society (pp. 219\u2013226).","DOI":"10.1145\/3306618.3317950"},{"key":"6583_CR19","doi-asserted-by":"crossref","unstructured":"Guo, Z., Li, J., Xiao, T., Ma, Y., & Wang, S. (2023). Towards fair graph neural networks via graph counterfactual. In Proceedings of the 32nd ACM international conference on information and knowledge management (pp. 669\u2013678).","DOI":"10.1145\/3583780.3615092"},{"key":"6583_CR20","doi-asserted-by":"crossref","unstructured":"Han, H., Wang, W.-Y., & Mao, B.-H. (2005). Borderline-smote: A new over-sampling method in imbalanced data sets learning. In International conference on intelligent computing (pp. 878\u2013887). Springer.","DOI":"10.1007\/11538059_91"},{"key":"6583_CR21","unstructured":"Hardt, M., Price, E., & Srebro, N. (2016). Equality of opportunity in supervised learning. Advances in Neural Information Processing Systems, 29, 3315\u20133323."},{"key":"6583_CR22","unstructured":"Hort, M., Chen, Z., Zhang, J. M., Sarro, F., & Harman, M. (2022). Bias mitigation for machine learning classifiers: A comprehensive survey. arXiv preprint arXiv:2207.07068."},{"key":"6583_CR23","unstructured":"Ismail, A. A., Arik, S.\u00d6., Yoon, J., Taly, A., Feizi, S., & Pfister, T. (2022). Interpretable mixture of experts for structured data. arXiv preprint arXiv:2206.02107."},{"issue":"1","key":"6583_CR24","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1162\/neco.1991.3.1.79","volume":"3","author":"RA Jacobs","year":"1991","unstructured":"Jacobs, R. A., Jordan, M. I., Nowlan, S. J., & Hinton, G. E. (1991). Adaptive mixtures of local experts. Neural Computation, 3(1), 79\u201387.","journal-title":"Neural Computation"},{"key":"6583_CR25","doi-asserted-by":"publisher","unstructured":"Kamiran, F., Karim, A., & Zhang, X. (2012). Decision theory for discrimination-aware classification. In 2012 IEEE 12th international conference on data mining (pp. 924\u2013929). https:\/\/doi.org\/10.1109\/ICDM.2012.45.","DOI":"10.1109\/ICDM.2012.45"},{"issue":"1","key":"6583_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10115-011-0463-8","volume":"33","author":"F Kamiran","year":"2012","unstructured":"Kamiran, F., & Calders, T. (2012). Data preprocessing techniques for classification without discrimination. Knowledge and Information Systems, 33(1), 1\u201333.","journal-title":"Knowledge and Information Systems"},{"key":"6583_CR27","doi-asserted-by":"publisher","first-page":"10262","DOI":"10.1109\/ACCESS.2020.2964726","volume":"8","author":"I Khan","year":"2020","unstructured":"Khan, I., Zhang, X., Rehman, M., & Ali, R. (2020). A literature survey and empirical study of meta-learning for classifier selection. IEEE Access, 8, 10262\u201310281.","journal-title":"IEEE Access"},{"key":"6583_CR28","unstructured":"Kim, B., Khanna, R., & Koyejo, O. O. (2016). Examples are not enough, learn to criticize! criticism for interpretability. Advances in Neural Information Processing Systems,29, 2280\u20132288."},{"key":"6583_CR29","unstructured":"Kubat, M., & Matwin, S. (1997). Addressing the curse of imbalanced training sets: One-sided selection. In: Icml (Vol. 97, p. 179). Citeseer."},{"key":"6583_CR30","unstructured":"Kusner, M. J., Loftus, J., Russell, C., & Silva, R. (2017). Counterfactual fairness. Advances in Neural Information Processing Systems, 30, 4066\u20134076."},{"issue":"1","key":"6583_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/sdata.2017.171","volume":"4","author":"J Kuzilek","year":"2017","unstructured":"Kuzilek, J., Hlosta, M., & Zdrahal, Z. (2017). Open university learning analytics dataset. Scientific Data, 4(1), 1\u20138.","journal-title":"Scientific Data"},{"key":"6583_CR32","doi-asserted-by":"crossref","unstructured":"Laurikkala, J.(2001). Improving identification of difficult small classes by balancing class distribution. In Artificial intelligence in medicine: 8th conference on artificial intelligence in medicine in Europe, AIME 2001 Cascais, Portugal, July 1\u20134, 2001, Proceedings 8 (pp. 63\u201366). Springer.","DOI":"10.1007\/3-540-48229-6_9"},{"issue":"3","key":"6583_CR33","first-page":"1452","volume":"12","author":"T Le Quy","year":"2022","unstructured":"Le Quy, T., Roy, A., Iosifidis, V., Zhang, W., & Ntoutsi, E. (2022). A survey on datasets for fairness-aware machine learning. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 12(3), 1452.","journal-title":"Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery"},{"key":"6583_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.artint.2018.07.007","volume":"267","author":"T Miller","year":"2019","unstructured":"Miller, T. (2019). Explanation in artificial intelligence: Insights from the social sciences. Artificial Intelligence, 267, 1\u201338.","journal-title":"Artificial Intelligence"},{"key":"6583_CR35","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.dss.2014.03.001","volume":"62","author":"S Moro","year":"2014","unstructured":"Moro, S., Cortez, P., & Rita, P. (2014). A data-driven approach to predict the success of bank telemarketing. Decision Support Systems, 62, 22\u201331.","journal-title":"Decision Support Systems"},{"key":"6583_CR36","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1007\/s10844-015-0368-1","volume":"46","author":"K Napierala","year":"2016","unstructured":"Napierala, K., & Stefanowski, J. (2016). Types of minority class examples and their influence on learning classifiers from imbalanced data. Journal of Intelligent Information Systems, 46, 563\u2013597. https:\/\/doi.org\/10.1007\/s10844-015-0368-1","journal-title":"Journal of Intelligent Information Systems"},{"key":"6583_CR37","doi-asserted-by":"publisher","DOI":"10.1109\/TSE.2022.3220713","author":"K Peng","year":"2022","unstructured":"Peng, K., Chakraborty, J., & Menzies, T. (2022). Fairmask: Better fairness via model-based rebalancing of protected attributes. IEEE Transactions on Software Engineering. https:\/\/doi.org\/10.1109\/TSE.2022.3220713","journal-title":"IEEE Transactions on Software Engineering"},{"key":"6583_CR38","doi-asserted-by":"publisher","first-page":"3305","DOI":"10.1007\/s10994-023-06376-z","volume":"113","author":"A Pereira Barata","year":"2023","unstructured":"Pereira Barata, A., Takes, F. W., Herik, H. J., & Veenman, C. J. (2023). Fair tree classifier using strong demographic parity. Machine Learning, 113, 3305\u20133324.","journal-title":"Machine Learning"},{"key":"6583_CR39","doi-asserted-by":"crossref","unstructured":"Perera, P., Nallapati, R., & Xiang, B. (2019). Ocgan: One-class novelty detection using gans with constrained latent representations. In Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition (CVPR).","DOI":"10.1109\/CVPR.2019.00301"},{"key":"6583_CR40","unstructured":"Pleiss, G., Raghavan, M., Wu, F., Kleinberg, J., & Weinberger, K. Q. (2017). On fairness and calibration. Advances in Neural Information Processing Systems, 30, 5680\u20135689."},{"key":"6583_CR41","first-page":"8583","volume":"34","author":"C Riquelme","year":"2021","unstructured":"Riquelme, C., Puigcerver, J., Mustafa, B., Neumann, M., Jenatton, R., Susano Pinto, A., Keysers, D., & Houlsby, N. (2021). Scaling vision with sparse mixture of experts. Advances in Neural Information Processing Systems, 34, 8583\u20138595.","journal-title":"Advances in Neural Information Processing Systems"},{"issue":"5","key":"6583_CR42","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1038\/s42256-019-0048-x","volume":"1","author":"C Rudin","year":"2019","unstructured":"Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature Machine Intelligence, 1(5), 206\u2013215.","journal-title":"Nature Machine Intelligence"},{"key":"6583_CR43","unstructured":"Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S. A., Binder, A., M\u00fcller, E., & Kloft, M. (2018). Deep one-class classification. In International conference on machine learning (pp. 4393\u20134402). PMLR"},{"key":"6583_CR44","unstructured":"Shazeer, N., Mirhoseini, A., Maziarz, K., Davis, A., Le, Q., Hinton, G., & Dean, J. (2017). Outrageously large neural networks: The sparsely-gated mixture-of-experts layer. arXiv preprint arXiv:1701.06538."},{"key":"6583_CR45","doi-asserted-by":"crossref","unstructured":"Stefanowski, J. (2013). Overlapping, rare examples and class decomposition in learning classifiers from imbalanced data. In Emerging paradigms in machine learning (pp. 277\u2013306). Springer.","DOI":"10.1007\/978-3-642-28699-5_11"},{"key":"6583_CR46","doi-asserted-by":"crossref","unstructured":"Strack, B., DeShazo, J. P., Gennings, C., Olmo, J. L., Ventura, S., Cios, K. J., Clore, J. N., et al. (2014). Impact of hba1c measurement on hospital readmission rates: Analysis of 70,000 clinical database patient records. BioMed Research International, 2014, 781670\u2013781680.","DOI":"10.1155\/2014\/781670"},{"key":"6583_CR47","unstructured":"Vanschoren, J. (2018). Meta-learning: A survey. arXiv preprint arXiv:1810.03548."},{"key":"6583_CR48","unstructured":"Wightman, L .F. (1998). Lsac national longitudinal bar passage study. lSAC research report series."},{"key":"6583_CR49","unstructured":"Xian, R., Yin, L., & Zhao, H. (2023). Fair and optimal classification via post-processing. In International conference on machine learning, (pp. 37977\u201338012). PMLR."},{"issue":"2","key":"6583_CR50","doi-asserted-by":"publisher","first-page":"2473","DOI":"10.1016\/j.eswa.2007.12.020","volume":"36","author":"I.-C Yeh","year":"2009","unstructured":"Yeh, I. .-C., & Lien, C. .-h. (2009). The comparisons of data mining techniques for the predictive accuracy of probability of default of credit card clients. Expert Systems with Applications, 36(2), 2473\u20132480.","journal-title":"Expert Systems with Applications"},{"issue":"8","key":"6583_CR51","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1109\/TNNLS.2012.2200299","volume":"23","author":"SE Yuksel","year":"2012","unstructured":"Yuksel, S. E., Wilson, J. N., & Gader, P. D. (2012). Twenty years of mixture of experts. IEEE Transactions on Neural Networks and Learning Systems, 23(8), 1177\u20131193.","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"6583_CR52","unstructured":"Zafar, M. B., Valera, I., Rogriguez, M. G., & Gummadi, K. P. (2017). Fairness constraints: Mechanisms for fair classification. In Artificial intelligence and statistics (pp. 962\u2013970). PMLR."},{"key":"6583_CR54","doi-asserted-by":"crossref","unstructured":"Zhang, B. H., Lemoine, B., & Mitchell, M. (2018). Mitigating unwanted biases with adversarial learning. In Proceedings of the 2018 AAAI\/ACM conference on AI, ethics, and society (pp. 335\u2013340).","DOI":"10.1145\/3278721.3278779"},{"key":"6583_CR53","doi-asserted-by":"crossref","unstructured":"Zhang, W., Bifet, A., Zhang, X., Weiss, J. C., & Nejdl, W. (2021). Farf: A fair and adaptive random forests classifier. In Pacific-Asia conference on knowledge discovery and data mining (pp. 245\u2013256).","DOI":"10.1007\/978-3-030-75765-6_20"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-024-06583-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-024-06583-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-024-06583-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T17:31:20Z","timestamp":1723051880000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-024-06583-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,8]]},"references-count":54,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["6583"],"URL":"https:\/\/doi.org\/10.1007\/s10994-024-06583-2","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,8]]},"assertion":[{"value":"27 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 July 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}