[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-290877-105":59,"doc-detail-290877-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","distance-based-copying-of-machine-learning-classifiers-a-thesis","Distance-based copying of machine learning classifiers - A thesis","","Copying machine learning black-box classifiers enables practitioners to upgrade legacy models by enriching properties, changing architectures, or aligning systems with evolving AI transparency, privacy, and explainability requirements. When retraining the original model from scratch is infeasible due to constraints, distance-based copying offers an alternative. The work proposes using signed distances to the decision boundary instead of hard labels, with two algorithms to compute them. Experiments on synthetic and real problems assess success across evaluation metrics and show the distance quality and uncertainty potential.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/distance-based-copying-of-machine-learning-classifiers-a-thesis/290877/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/distance-based-copying-of-machine-learning-classifiers-a-thesis/290877.png","ImageObject",300,407,{"name":92,"@type":93},"Skyler","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-18","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does distance-based copying address?","Question",{"text":112,"@type":113},"It targets the challenge of copying a black-box classifier’s decision boundary when only hard labels are available and the original training data or retraining is not feasible.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the thesis differ from hard-label copying methods?",{"text":117,"@type":113},"It replaces black-box hard labels with signed distances to the decision boundary, using two algorithms to compute those distances.",{"name":119,"@type":110,"acceptedAnswer":120},"What evidence supports the proposed approach?",{"text":121,"@type":113},"A series of experiments on synthetic datasets and real problems evaluates success across multiple settings and metrics, and validates the predicted distances as uncertainty measures.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},290877,1789642861,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144,"preview_page_count":4},2336464648746,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","UNIVERSITAT DE BARCELONA  \nFUNDAMENTAL PRINCIPLES OF DATA SCIENCE MASTER ’S  \nTHESIS  \nDistance-based copying of machine learning classifiers  \nAuthor:  \nRubén JIMÉNEZ LUMBRERAS  \nSupervisor:  \nDr. Oriol PUJOL VILA  \nA thesis submitted in partial fulfillment of the requirements for the degree of MSc in Fundamental Principles of Data Science  \nin the  \nFacultat de Matemàtiques i Informàtica  \nJanuary 10, 2026  \niii  \nUNIVERSITAT DE BARCELONA  \nAbstract  \nFacultat de Matemàtiques i Informàtica  \nMSc  \nDistance-based copying of machine learning classifiers  \nby Rubén JIMÉNEZ LUMBRERAS  \nCopying machine learning black box classifiers is a key framework that allows practitioners to upgrade their old models, enriching them with new properties, changing their architectures or adapting them to comply with the current AI legislations. Thanks to the copying techniques and assumptions, these improvements can be done even in settings where retraining the original system from scratch is not possible, due to resource, protocol or availability constraints. In this work, we propose the use of signed distances to the decision boundary as a replacement of the blackbox hard labels used to build the copies, and introduce two different algorithms to compute these distances. In addition, we observe that distance-based copying could behave as a model-agnostic regularization technique and develop a flexible framework to reduce the generalization error of the copies. Then, we validate these proposals through a series of experiments on synthetic datasets and real problems. Results show that distance-based copying is successful across multiple relevant settings and evaluation metrics. Furthermore, results also validate the quality of the predicted distances and their potential as uncertainty measures.  \nv  \nAcknowledgements  \nI would like to deeply thank Dr. Oriol Pujol Vila for all the support, time, dedication and help he has given me throughout this project, which has made it possible.  \nI would also like to thank my master’s classmates and professors for their help and the good moments I had the pleasure of sharing with them during this past year.  \nFinally, I also want to thank my family for all their support, help, and advice. Thanks to them, I have been able to get to where I am and become who I am.  \nvii  \nContents  \nAbstract iii  \nAcknowledgements v  \n1 Introduction 1  \n2 Related Work 3  \n3 Distance-based copying 5  \n3.1 Proposal .................................... 5  \n3.2 Algorithms ................................... 6  \n3.3 Regularization effect ............................. 7  \n4 Empirical validation 9  \n4.1 Setup and experiments ............................ 9  \n4.2 Results ..................................... 11  \n4.2.1 Experiment 1 . Global comparison ................. 11  \n4.2.2 Experiment 2 . Regularization effect ................ 13  \n4.2.3 Experiment 3 . Quality of the distances ............... 14  \n5 Discussion 15  \n6 Conclusions 17  \nA Algorithms 19  \nB Supplemental material. Tables 21  \nC Supplemental material. Figures 25  \nD Two-stage distance-copying extension 41  \nE Source Code Repository 49  \nBibliography 51  \n1  \nChapter 1  \nIntroduction  \nNowadays, society is going through a period of very fast development of machine learning models, where the state of the art is evolving at an increasing rate (Lu, 2019; Azad and Banu, 2024) . Parallel to this expansion, new legislation about transparency (Lund et al., 2025), privacy (Ye et al., 2024; Korobenko, Nikiforova, and Sharma, 2024; Parinandi et al., 2024) or explainability (Panigutti et al., 2023; Nannini, Balayn, and Smith, 2023; Gade et al., 2019) is also being implemented around the world.  \nAs a consequence, it is vital for practitioners to be able to react to these changes and keep themselves up to date, upgrading their old models to more suitable architectures or adapting them to comply with new legislation (Wong, Chong, and Aspegren, 2023) . Nevertheless, these are challeng","cbCairX5E1cGL6WO","https://ap.wps.com/l/cbCairX5E1cGL6WO","pdf",51740718,62,"English","# 1 Introduction\n# 2 Related Work\n# 3 Distance-based copying\n## 3.1 Proposal\n## 3.2 Algorithms\n## 3.3 Regularization effect\n# 4 Empirical validation\n## 4.1 Setup and experiments\n## 4.2 Results\n## 4.2.1 Experiment 1 . Global comparison\n## 4.2.2 Experiment 2 . Regularization effect\n## 4.2.3 Experiment 3 . Quality of the distances\n# 5 Discussion\n# 6 Conclusions\n# A Algorithms\n# B Supplemental material. Tables\n# C Supplemental material. Figures\n# D Two-stage distance-copying extension\n# E Source Code Repository\n# Bibliography","[{\"question\":\"What problem does distance-based copying address?\",\"answer\":\"It targets the challenge of copying a black-box classifier’s decision boundary when only hard labels are available and the original training data or retraining is not feasible.\"},{\"question\":\"How does the thesis differ from hard-label copying methods?\",\"answer\":\"It replaces black-box hard labels with signed distances to the decision boundary, using two algorithms to compute those distances.\"},{\"question\":\"What evidence supports the proposed approach?\",\"answer\":\"A series of experiments on synthetic datasets and real problems evaluates success across multiple settings and metrics, and validates the predicted distances as uncertainty measures.\"}]","Distance-based copying of machine learning classifiers - A thesis | PDF",156]