{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T16:49:09Z","timestamp":1761324549498,"version":"3.37.3"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T00:00:00Z","timestamp":1698192000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T00:00:00Z","timestamp":1698192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100009042","name":"Universidad de Sevilla","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100009042","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Data Anal Classif"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Counterfactual explanations have become a very popular interpretability tool to understand and explain how complex machine learning models make decisions for individual instances. Most of the research on counterfactual explainability focuses on tabular and image data and much less on models dealing with functional data. In this paper, a counterfactual analysis for functional data is addressed, in which the goal is to identify the samples of the dataset from which the counterfactual explanation is made of, as well as how they are combined so that the individual instance and its counterfactual are as close as possible. Our methodology can be used with different distance measures for multivariate functional data and is applicable to any score-based classifier. We illustrate our methodology using two different real-world datasets, one univariate and another multivariate.<\/jats:p>","DOI":"10.1007\/s11634-023-00563-5","type":"journal-article","created":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T13:01:37Z","timestamp":1698238897000},"page":"981-1000","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A new model for counterfactual analysis for functional data"],"prefix":"10.1007","volume":"18","author":[{"given":"Emilio","family":"Carrizosa","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7715-3756","authenticated-orcid":false,"given":"Jasone","family":"Ram\u00edrez-Ayerbe","sequence":"additional","affiliation":[]},{"given":"Dolores","family":"Romero Morales","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,10,25]]},"reference":[{"key":"563_CR1","doi-asserted-by":"publisher","first-page":"104861","DOI":"10.1016\/j.jmva.2021.104861","volume":"189","author":"G Aneiros","year":"2022","unstructured":"Aneiros G, Horov\u00e1 I, Hu\u0161kov\u00e1 M, Vieu P (2022) On functional data analysis and related topics. J Multivar Anal 189:104861","journal-title":"J Multivar Anal"},{"key":"563_CR2","doi-asserted-by":"publisher","unstructured":"Ates E, Aksar B, Leung VJ, Coskun AK (2021) Counterfactual explanations for multivariate time series. In: 2021 international conference on applied artificial intelligence (ICAPAI), pp 1\u20138. https:\/\/doi.org\/10.1109\/ICAPAI49758.2021.9462056","DOI":"10.1109\/ICAPAI49758.2021.9462056"},{"issue":"2","key":"563_CR3","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1016\/j.ejor.2021.04.016","volume":"295","author":"S Ben\u00edtez-Pe\u00f1a","year":"2021","unstructured":"Ben\u00edtez-Pe\u00f1a S, Carrizosa E, Guerrero V, Jim\u00e9nez-Gamero M, Mart\u00ednBarrag\u00e1n B, Molero-R\u00edo C, Ram\u00edrez-Cobo P, Romero Morales D, Sillero-Denamiel M (2021) On sparse ensemble methods: an application to short-term predictions of the evolution of COVID-19. Eur J Oper Res 295(2):648\u2013663","journal-title":"Eur J Oper Res"},{"key":"563_CR4","first-page":"359","volume":"10","author":"DJ Berndt","year":"1994","unstructured":"Berndt DJ, Clifford J (1994) Using dynamic time warping to find patterns in time series. KDD Workshop 10:359\u2013370","journal-title":"KDD Workshop"},{"issue":"7","key":"563_CR5","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1007\/s10994-017-5633-9","volume":"106","author":"D Bertsimas","year":"2017","unstructured":"Bertsimas D, Dunn J (2017) Optimal classification trees. Mach Learn 106(7):1039\u20131082","journal-title":"Mach Learn"},{"issue":"2","key":"563_CR6","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1214\/15-AOS1388","volume":"44","author":"D Bertsimas","year":"2016","unstructured":"Bertsimas D, King A, Mazumder R (2016) Best subset selection via a modern optimization lens. Ann Stat 44(2):813\u2013852","journal-title":"Ann Stat"},{"issue":"1","key":"563_CR7","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/j.ejor.2018.11.024","volume":"275","author":"R Blanquero","year":"2019","unstructured":"Blanquero R, Carrizosa E, Jim\u00e9nez-Cordero A, Mart\u00edn-Barrag\u00e1n B (2019) Functional-bandwidth kernel for support vector machine with functional data: an alternating optimization algorithm. Eur J Oper Res 275(1):195\u2013207","journal-title":"Eur J Oper Res"},{"key":"563_CR8","doi-asserted-by":"publisher","first-page":"106152","DOI":"10.1016\/j.cor.2023.106152","volume":"152","author":"R Blanquero","year":"2023","unstructured":"Blanquero R, Carrizosa E, Molero-R\u00edo C, Romero Morales D (2023) On optimal regression trees to detect critical intervals for multivariate functional data. Comput Oper Res 152:106152","journal-title":"Comput Oper Res"},{"issue":"1","key":"563_CR9","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1010933404324","volume":"45","author":"L Breiman","year":"2001","unstructured":"Breiman L (2001) Random forests. Mach Learn 45(1):5\u201332","journal-title":"Mach Learn"},{"key":"563_CR10","doi-asserted-by":"publisher","first-page":"102543","DOI":"10.1016\/j.omega.2021.102543","volume":"107","author":"E Carrizosa","year":"2022","unstructured":"Carrizosa E, Kurishchenko K, Mar\u00edn A, Romero Morales D (2022) Interpreting clusters by prototype optimization. Omega 107:102543","journal-title":"Omega"},{"key":"563_CR12","doi-asserted-by":"crossref","unstructured":"Carrizosa E, Ram\u00edrez Ayerbe J, Romero Morales D (2023) Mathematical optimization modelling for group counterfactual explanations (Tech. Rep.): IMUS, Sevilla, Spain. https:\/\/www.researchgate.net\/publication\/368958766_Mathematical_Optimization_Modelling_for_Group_Counterfactual_Explanations","DOI":"10.1016\/j.ejor.2024.01.002"},{"key":"563_CR11","doi-asserted-by":"publisher","first-page":"121954","DOI":"10.1016\/j.eswa.2023.121954","volume":"238","author":"E Carrizosa","year":"2024","unstructured":"Carrizosa E, Ram\u00edrez-Ayerbe J, Romero Morales D (2024) Generating collective counterfactual explanations in score-based classification via mathematical optimization. Expert Syst Appl 238:121954","journal-title":"Expert Syst Appl"},{"key":"563_CR13","doi-asserted-by":"publisher","first-page":"1450","DOI":"10.1287\/opre.1080.0573","volume":"56","author":"W Chaovalitwongse","year":"2008","unstructured":"Chaovalitwongse W, Fan Y, Sachdeo R (2008) Novel optimization models for abnormal brain activity classification. Oper Res 56:1450\u20131460","journal-title":"Oper Res"},{"key":"563_CR14","doi-asserted-by":"publisher","unstructured":"Chen T, Guestrin C (2016) XGBoost: A scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. ACM, New York, pp 785\u2013794. Retrieved from https:\/\/doi.org\/10.1145\/2939672.2939785","DOI":"10.1145\/2939672.2939785"},{"issue":"6","key":"563_CR15","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.1109\/JAS.2019.1911747","volume":"6","author":"HA Dau","year":"2019","unstructured":"Dau HA, Bagnall A, Kamgar K, Yeh C-CM, Zhu Y, Gharghabi S, Ratanamahatana CA, Keogh E (2019) The UCR time series archive. IEEE\/CAA J Autom Sin 6(6):1293\u20131305","journal-title":"IEEE\/CAA J Autom Sin"},{"key":"563_CR16","doi-asserted-by":"crossref","unstructured":"Delaney E, Greene D, Keane MT (2021) Instance-based counterfactual explanations for time series classification. In: International conference on case-based reasoning, pp 32\u201347","DOI":"10.1007\/978-3-030-86957-1_3"},{"issue":"1","key":"563_CR17","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1145\/3359786","volume":"63","author":"M Du","year":"2019","unstructured":"Du M, Liu N, Hu X (2019) Techniques for interpretable machine learning. Commun ACM 63(1):68\u201377","journal-title":"Commun ACM"},{"key":"563_CR18","doi-asserted-by":"publisher","first-page":"113141","DOI":"10.1016\/j.dss.2019.113141","volume":"127","author":"C Eiras-Franco","year":"2019","unstructured":"Eiras-Franco C, Guijarro-Berdinas B, Alonso-Betanzos A, Bahamonde A (2019) A scalable decision-tree-based method to explain interactions in dyadic data. Decis Support Syst 127:113141","journal-title":"Decis Support Syst"},{"issue":"1","key":"563_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2379776.2379788","volume":"45","author":"P Esling","year":"2012","unstructured":"Esling P, Agon C (2012) Time-series data mining. ACM Comput Surv (CSUR) 45(1):1\u201334","journal-title":"ACM Comput Surv (CSUR)"},{"issue":"6","key":"563_CR20","doi-asserted-by":"publisher","first-page":"4173","DOI":"10.1287\/mnsc.2021.4065","volume":"68","author":"R Fu","year":"2022","unstructured":"Fu R, Aseri M, Singh P, Srinivasan K (2022) Un fair machine learning algorithms. Manage Sci 68(6):4173\u20134195","journal-title":"Manage Sci"},{"issue":"2","key":"563_CR21","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1504\/IJAPR.2017.085315","volume":"4","author":"N Ghouaiel","year":"2017","unstructured":"Ghouaiel N, Marteau P-F, Dupont M (2017) Continuous pattern detection and recognition in stream\u2014a benchmark for online gesture recognition. Int J Appl Pattern Recogn 4(2):146\u2013160","journal-title":"Int J Appl Pattern Recogn"},{"issue":"3","key":"563_CR22","first-page":"50","volume":"38","author":"B Goodman","year":"2017","unstructured":"Goodman B, Flaxman S (2017) European Union regulations on algorithmic decision-making and a right to explanation. AI Mag 38(3):50\u201357","journal-title":"AI Mag"},{"key":"563_CR23","doi-asserted-by":"crossref","unstructured":"Guidotti R (2022) Counterfactual explanations and how to find them: literature review and benchmarking. Data Min Knowl Discov (forthcoming)","DOI":"10.1007\/s10618-022-00831-6"},{"key":"563_CR24","unstructured":"Gurobi Optimization L (2021) Gurobi optimizer reference manual. Retrieved from http:\/\/www.gurobi.com"},{"key":"563_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-58821-6","volume-title":"Pyomo-optimization modeling in Python","author":"WE Hart","year":"2017","unstructured":"Hart WE, Laird CD, Watson J-P, Woodruff DL, Hackebeil GA, Nicholson BL, Siirola JD (2017) Pyomo-optimization modeling in Python, vol 67, 2nd edn. Springer, New York","edition":"2"},{"issue":"3","key":"563_CR26","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s12532-011-0026-8","volume":"3","author":"WE Hart","year":"2011","unstructured":"Hart WE, Watson J-P, Woodruff DL (2011) Pyomo: modeling and solving mathematical programs in Python. Math Program Comput 3(3):219\u2013260","journal-title":"Math Program Comput"},{"issue":"2","key":"563_CR27","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1214\/088342306000000132","volume":"21","author":"W Jank","year":"2006","unstructured":"Jank W, Shmueli G (2006) Functional data analysis in electronic commerce research. Stat Sci 21(2):155\u2013166","journal-title":"Stat Sci"},{"issue":"5","key":"563_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3527848","volume":"55","author":"A-H Karimi","year":"2022","unstructured":"Karimi A-H, Barthe G, Sch\u00f6lkopf B, Valera I (2022) A survey of algorithmic recourse: contrastive explanations and consequential recommendations. ACM Comput Surv 55(5):1\u201329","journal-title":"ACM Comput Surv"},{"key":"563_CR29","doi-asserted-by":"crossref","unstructured":"Keogh E, Wei L, Xi X, Lonardi S, Shieh J, Sirowy S (2006) Intelligent icons: integrating lite-weight data mining and visualization into GUI operating systems. In: Sixth international conference on data mining (ICDM\u201906), pp 912\u2013916","DOI":"10.1109\/ICDM.2006.90"},{"issue":"1","key":"563_CR30","doi-asserted-by":"publisher","first-page":"2522","DOI":"10.1038\/s42256-019-0138-9","volume":"2","author":"S Lundberg","year":"2020","unstructured":"Lundberg S, Erion G, Chen H, DeGrave A, Prutkin J, Nair B, Katz R, Himmelfarb J, Bansal N, Lee S-I (2020) From local explanations to global understanding with explainable AI for trees. Nat Mach Intell 2(1):2522\u20135839","journal-title":"Nat Mach Intell"},{"key":"563_CR31","unstructured":"Lundberg SM, Lee S-I (2017) A unified approach to interpreting model predictions. In: Proceedings of the 31st international conference on neural information processing systems, pp 4768\u20134777"},{"issue":"1","key":"563_CR32","doi-asserted-by":"publisher","first-page":"73","DOI":"10.25300\/MISQ\/2014\/38.1.04","volume":"38","author":"D Martens","year":"2014","unstructured":"Martens D, Provost F (2014) Explaining data-driven document classifications. MIS Q 38(1):73\u201399","journal-title":"MIS Q"},{"issue":"1","key":"563_CR33","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.ejor.2012.08.017","volume":"232","author":"B Mart\u00edn-Barrag\u00e1n","year":"2014","unstructured":"Mart\u00edn-Barrag\u00e1n B, Lillo R, Romo J (2014) Interpretable support vector machines for functional data. Eur J Oper Res 232(1):146\u2013155","journal-title":"Eur J Oper Res"},{"key":"563_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. Artif Intell 267:1\u201338","journal-title":"Artif Intell"},{"key":"563_CR35","doi-asserted-by":"crossref","unstructured":"Mohammadi K, Karimi A-H, Barthe G, Valera I (2021) Scaling guarantees for nearest counterfactual explanations. In: Proceedings of the 2021 AAAI\/ACM conference on AI, ethics, and society, pp 177\u2013187","DOI":"10.1145\/3461702.3462514"},{"key":"563_CR36","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1007\/s11634-020-00418-3","volume":"14","author":"Y Ramon","year":"2020","unstructured":"Ramon Y, Martens D, Provost F, Evgeniou T (2020) A comparison of instance-level counterfactual explanation algorithms for behavioral and textual data: SEDC, LIME-C and SHAP-C. Adv Data Anal Classif 14:801\u2013819","journal-title":"Adv Data Anal Classif"},{"key":"563_CR37","doi-asserted-by":"publisher","unstructured":"Ramsay JO (2006) Functional data analysis. In: Encyclopedia of statistical sciences, vol 4. https:\/\/doi.org\/10.1002\/0471667196.ess3138","DOI":"10.1002\/0471667196.ess3138"},{"key":"563_CR38","doi-asserted-by":"crossref","unstructured":"Ribeiro MT, Singh S, Guestrin C (2016) \u201cWhy should i trust you?\u201d Explaining the predictions of any classifier. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp 1135\u20131144","DOI":"10.1145\/2939672.2939778"},{"issue":"1","key":"563_CR39","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1287\/mksc.1080.0382","volume":"28","author":"A Sood","year":"2009","unstructured":"Sood A, James GM, Tellis GJ (2009) Functional regression: a new model for predicting market penetration of new products. Mark Sci 28(1):36\u201351","journal-title":"Mark Sci"},{"issue":"11","key":"563_CR40","doi-asserted-by":"publisher","first-page":"6716","DOI":"10.1287\/mnsc.2020.3854","volume":"67","author":"N Sunar","year":"2021","unstructured":"Sunar N, Swaminathan JM (2021) Net-metered distributed renewable energy: a peril for utilities? Manag Sci 67(11):6716\u20136733","journal-title":"Manag Sci"},{"key":"563_CR41","doi-asserted-by":"crossref","unstructured":"Tolkachev G, Mell S, Zdancewic S, Bastani O (2022) Counterfactual explanations for natural language interfaces. In: Proceedings of the 60th annual meeting of the association for computational linguistics, pp 113\u2013118","DOI":"10.18653\/v1\/2022.acl-short.14"},{"key":"563_CR42","unstructured":"Verma S, Dickerson J, Hines K (2020) Counterfactual explanations for machine learning: a review. arXiv preprint arXiv:2010.10596"},{"key":"563_CR43","first-page":"841","volume":"31","author":"S Wachter","year":"2017","unstructured":"Wachter S, Mittelstadt B, Russell C (2017) Counterfactual explanations without opening the black box: automated decisions and the GDPR. Harv JL Tech 31:841","journal-title":"Harv JL Tech"},{"issue":"1","key":"563_CR44","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1145\/1882471.1882478","volume":"12","author":"Z Xing","year":"2010","unstructured":"Xing Z, Pei J, Keogh E (2010) A brief survey on sequence classification. ACM SIGKDD Explor Newsl 12(1):40\u201348","journal-title":"ACM SIGKDD Explor Newsl"},{"key":"563_CR45","doi-asserted-by":"publisher","first-page":"113715","DOI":"10.1016\/j.dss.2021.113715","volume":"155","author":"D Zhdanov","year":"2022","unstructured":"Zhdanov D, Bhattacharjee S, Bragin MA (2022) Incorporating FAT and privacy aware AI modeling approaches into business decision making frameworks. Decis Support Syst 155:113715","journal-title":"Decis Support Syst"},{"issue":"1","key":"563_CR46","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1287\/opre.2020.2005","volume":"69","author":"Z Zheng","year":"2021","unstructured":"Zheng Z, Lv J, Lin W (2021) Nonsparse learning with latent variables. Oper Res 69(1):346\u2013359","journal-title":"Oper Res"}],"container-title":["Advances in Data Analysis and Classification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-023-00563-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11634-023-00563-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11634-023-00563-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T08:15:05Z","timestamp":1732176905000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11634-023-00563-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,25]]},"references-count":46,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["563"],"URL":"https:\/\/doi.org\/10.1007\/s11634-023-00563-5","relation":{},"ISSN":["1862-5347","1862-5355"],"issn-type":[{"type":"print","value":"1862-5347"},{"type":"electronic","value":"1862-5355"}],"subject":[],"published":{"date-parts":[[2023,10,25]]},"assertion":[{"value":"13 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 September 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 October 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors state that there are not financial conflicts of interest related to the paper and certify that they are complying with the journal\u2019s ethical policies.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}