[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117525-en":3,"doc-seo-117525-105":30,"detail-sidebar-cat-0-en-105":92},{"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},117525,1099514067438,"River Wang","https://ap-avatar.wpscdn.com/avatar/100002539ee87300030?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780474512215547542",8,"Research & Report","Probabilistic Numerics - Bayesian Quadrature and Human-AI Collaboration - Thesis","Machine learning for science often assumes expert inputs are error-free or treats experts as passive data providers, despite real scientific practice involving uncertainty. This thesis frames science as updating scientists’ beliefs from objective evidence, with algorithms as encoded opinions. It studies alignment of algorithms with human beliefs and desiderata using Probabilistic Numerics for black-box optimization, integration, and inference via computational agents trained with diverse policies. It unifies tasks through Bayesian data compression and targets synchronization at policy and modelling levels for improved flexibility, adaptability, and belief communication across domains.","Probabilistic Numerics: Bayesian Quadrature and Human-AI Collaboration  \nMasaki Adachi St Catherine’s College University of Oxford  \nA thesis submitted for the degree of Doctor of Philosophy  \nHilary 2025  \nAcknowledgements  \nCompleting my DPhil at my dream place, working with wonderful people, has been a life-changing experience. I am deeply grateful to everyone who helped my research, social activities, and the funding that made this journey possible.  \nThank you to my wife, Aki, for her unwavering support and understanding, even in the face of my sudden decision to return to school on the other side of the world and live apart for three years. I am also deeply grateful to my family—Toshifumi, Kaori, and Akane—and to all my friends, particularly to Yuki and Juliusz for their steadfast encouragement and support.  \nI am profoundly grateful to my advisers, Mike Osborne and Dave Howey, for their unwavering support, guidance, and mentorship throughout my DPhil journey. Working with you both has been an incredible privilege and joy, and it has truly been one of the greatest assets of my life. Mike evangelised me to embrace Bayesian thinking and consistently supported me in pursuing my interests, while Dave instilled in me the importance of simplicity and focusing on the problem itself rather than the method, as an engineer should. I look forward to continuing our collaboration and hope to offer my support in the future, just as you both supported me during my DPhil.  \nI have been blessed with many talented co-authors and friends, including Satoshi Hayakawa, Siu Lun (Alan) Chau, Wenjie Xu, Juliusz Ziomek, Csaba Tóth, Joachim Schaeffer, Yuxin Lin, Philipp Dechent, Martin Jørgensen, Vu Nyguen, Pierre Osselin, Xingchen Wan, Masahiro Fujisawa, Yannick Kuhn, Colin N. Jones, Birger Horstmann, and Harald Oberhauser, to name a few. Thanks to all my coauthors, lab colleagues, and friends. A special note of gratitude goes to Satoshi and Alan, whose inspiration and support made my DPhil journey an incredibly joyful experience.  \nI am deeply grateful to the Clarendon Scholarship, Oxford-Kobe Scholarship, Watanabe Scholarship, and British Council Japan Association Scholarship for their financial support, which enabled me to pursue my studies in Oxford and engage in academic activities.  \nI would like to express my sincere thanks to my colleagues at Toyota Motor Corporation for supporting my return to academia, especially Kunihiro Nobuhara, Hirohito Hirata, and Hiroaki Okuchi for their continuous encouragement and guidance.  \nI am profoundly thankful to my examiners, Prof. Philipp Hennig and Prof. Xiaowen Dong, for their thoughtful and insightful evaluation of my thesis. I also extend my gratitude to Prof. Jacob Foerster, Prof. Tom Rainforth, Prof. Stephen Roberts, and Prof. Charles Monroe for their valuable feedback during my transfer and confirmation stages. Special thanks to the anonymous reviewers of my papers; your constructive critiques significantly improved the quality of this thesis.  \nI am thankful to Dr. Krikamol Muandet for hosting and mentoring me during my two-month visit at CISPA in Saarbrücken, Germany. It was an unforgettable experience where I gained valuable insights into identifying impactful research topics, fostering effective collaborations, and exploring concepts in economics and imprecise probability. I would also like to extend my heartfelt thanks to Alan, Anurag, Kiet, Rattaya, Swathi, and Saptarshi for making my time in Saarbrücken both enjoyable and memorable.  \nI would like to extend my heartfelt gratitude to Dr. Emtiyaz Khan for hosting me during my three-month internship at RIKEN AIP in Tokyo, Japan. Special thanks to a member of Approximate Bayesian Inference Team-Thomas, Yohan, Christopher, Kego, Hugo, Sin-Han, Anita, Bai, Eiki, Marco, Hyungi, Rin, Alex, Adrian– and particularly for Yohan for being a mentor.  \nA special thank you to the BatteryDEV team—Joachim, Simon, Raymond, and Anoushka—for the unforgettable ","cbCaivVNZdM0Jjq5","https://ap.wps.com/l/cbCaivVNZdM0Jjq5","pdf",29780976,1,250,"English","en",105,"# Abstract\n## Problem setting: human uncertainty and belief updates\n## Probabilistic Numerics framework for scientific ML\n## Bayesian quadrature as unified solver and Bayesian data compression\n## Policy-level unification across tasks\n## Modelling-level communication between agents and users","[{\"question\":\"Why does the thesis emphasize uncertainty in human scientific expertise?\",\"answer\":\"It argues that, unlike many machine-learning-for-science approaches, human experts face uncertainty in their processes, requiring a collaboration that accounts for both human and algorithmic beliefs.\"},{\"question\":\"What framework does the thesis use to align algorithms with human beliefs?\",\"answer\":\"It uses Probabilistic Numerics, treating scientific tasks like optimization, integration, and inference as machine-learning problems handled by computational agents with diverse policies.\"},{\"question\":\"How does the thesis unify multiple scientific tasks under one perspective?\",\"answer\":\"It focuses on Bayesian quadrature as a unified solver and interprets it as Bayesian data compression, where representative points propagate uncertainty in distributional estimates across tasks.\"}]","Probabilistic Numerics - 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