[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120622-en":3,"doc-seo-120622-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120622,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Frontiers of Statistics and Machine Learning - 2025 Oberwolfach Report","Workshop report Frontiers of Statistics and Machine Learning from Oberwolfach (Report No. 17/2025, March 23–28, 2025) unites leading and emerging researchers at the intersection of mathematical statistics and theoretical machine learning. It synthesizes the state of the art and advances the frontiers by focusing on three key themes: robustness and model misspecification, statistical theory for neural networks, and statistical theory for stochastic processes. The program features talks and junior presentations, and frames progress toward theory that supports modern AI methods.","Mathematisches Forschungsinstitut Oberwolfach  \nReport No. 17/2025  \nDOI: 10.4171/OWR/2025/17  \nFrontiers of Statistics and Machine Learning  \nOrganized by Marc Ho􀀋mann, Paris Richard J. Samworth, Cambridge UK  \nJohannes Schmidt-Hieber, Enschede  \nClaudia Strauch, Heidelberg  \n23 March – 28 March 2025  \nAbstract. AI is currently the central theme in science. Whereas the underlying algorithms rely on rather simple mathematical operations such as matrix-vector multiplications and applying non-linearities componentwise, deriving a theoretical understanding proves to be extremely challenging. To identify synergies between the 􀀌elds of mathematical statistics and theoretical machine learning, the workshop brought together leading researchers and rising stars who are tackling core challenges at the intersection of these 􀀌elds.  \nWe have identi􀀌ed the topics of robustness and model misspeci􀀌cation, statistical theory for neural networks and statistics for stochastic processes as three key themes that underpin increasingly many current developments. These topics were the focus of the talks and research that was carried out during  \nthe Oberwolfach week.  \nMathematics Subject Classi􀀌cation (2020): 62G05, 62G08, 62G20 .  \nLicense: Unless otherwise noted, the content of this report is licensed under CC BY SA 4.0 .  \nIntroduction by the Organizers  \nThe workshop Frontiers of Statistics and Machine Learning was attended by 47 participants (46 on site and one online) . The workshop brought together researchers with diverse backgrounds. The participants came from universities in the US, Japan, and Europe. The event featured around 22 talks and we organized an evening session with short presentations by junior participants (their abstracts are also included in this report) . The talks sparked numerous questions and (follow-up) discussions.  \n754 Oberwolfach Report 17/2025  \nUntil recently, statistics and machine learning were developed by nearly disjoint communities. Due to these independent developments, data science/machine learning and statistics di􀀋er in their approaches to data problems. This distinction is highlighted in Leo Breiman’s “Two cultures” [1] . While data science starts with speci􀀌c benchmark data sets and data competitions, statistics begins with the modelling of the sampling process. The more pragmatic, engineering-oriented approach of data scientists has a particular advantage in dealing with complex data structures where statistical modelling is unclear, often leading to better procedures. Conversely, statistics can squeeze out more information if the data distribution can be modelled. In this case one can often say more about uncertainty quanti􀀌cation, whether Bayesian or frequentist, which remains one of the challenging problems in data science.  \nUnifying these 􀀌elds with the goal to combine the di􀀋erent strengths is an ongoing and very active branch within statistics and machine learning. The workshop aimed to summarize the current state-of-the-art and push the frontiers of both statistics and machine learning.  \nWithin this 􀀌eld, we have identi􀀌ed three highly relevant subjects that are currently experiencing tremendous developments. These selected subjects are robustness, theory for neural networks and statistical theory for stochastic processes. All of them are intricately interconnected. While robustness to outliers is a classical topic within statistics with a well-developed mathematical theory, new ideas and concepts are currently developed to deal with very di􀀋erent forms of robustness, such as robustness of machine learning methods to a new distribution of the covariates during test time (covariate shift) or robustifying neural networks against adversarial attacks. Theory for neural networks has become a very active subject in the past years and combines elements from various areas in mathematics. Statistical theory for stochastic processes has a long tradition within mathematical statistics and the challenge ","cbCaig8nurK1dlSZ","https://ap.wps.com/l/cbCaig8nurK1dlSZ","pdf",451376,1,44,"English","en",105,"# Introduction by the Organizers\n## The two cultures and unification goals\n## Three key themes\n# Robustness and model misspecification\n## Motivation from modern AI data\n## Outliers, heavy tails, missing data, and covariate shift","[{\"question\":\"What three key themes does the workshop highlight?\",\"answer\":\"The workshop highlights robustness and model misspecification, statistical theory for neural networks, and statistical theory for stochastic processes. These topics are presented as tightly interconnected and driving many current developments.\"},{\"question\":\"Why is robustness and model misspecification especially important for contemporary AI?\",\"answer\":\"Simple models underlying classical thinking about small, clean datasets may no longer fit large-scale AI data. Real data can be messy due to differing collection conditions, missingness, and corruption, making traditional model checks infeasible.\"},{\"question\":\"How does the report describe the difference between statistics and data science/machine learning?\",\"answer\":\"It contrasts statistics starting from modeling the sampling process with data science beginning from benchmark datasets and data competitions. The report argues that pragmatic engineering approaches can help with complex structures, while statistical modeling can improve uncertainty quantification.\"}]","Frontiers of Statistics and Machine Learning - 2025 Oberwolfach Report | PDF",1785730945,111,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"frontiers-of-statistics-and-machine-learning-2025-oberwolfach-report","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/frontiers-of-statistics-and-machine-learning-2025-oberwolfach-report/120622/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What three key themes does the workshop highlight?","Question",{"text":75,"@type":76},"The workshop highlights robustness and model misspecification, statistical theory for neural networks, and statistical theory for stochastic processes. These topics are presented as tightly interconnected and driving many current developments.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is robustness and model misspecification especially important for contemporary AI?",{"text":80,"@type":76},"Simple models underlying classical thinking about small, clean datasets may no longer fit large-scale AI data. Real data can be messy due to differing collection conditions, missingness, and corruption, making traditional model checks infeasible.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the report describe the difference between statistics and data science/machine learning?",{"text":84,"@type":76},"It contrasts statistics starting from modeling the sampling process with data science beginning from benchmark datasets and data competitions. The report argues that pragmatic engineering approaches can help with complex structures, while statistical modeling can improve uncertainty quantification.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]