[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125329-en":3,"doc-seo-125329-105":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":4,"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},125329,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Scalable Machine Learning Algorithms using Path Signatures - Doctor of Philosophy Thesis","In this thesis, integration of path signatures—a mathematical object rooted in rough path theory—with scalable machine learning algorithms is used to address challenges in sequential and structured data modelling. Path signatures are developed as a hierarchical feature representation for dynamics with theoretical robustness and practical approximations. Gaussian process embeddings, a Seq2Tens low-rank framework, scalable graph extensions via hypo-elliptic diffusions, and random-feature signature methods are combined with theory and experiments for efficient learning.","Scalable Machine Learning Algorithms using Path Signatures  \nCsaba Tóth  \nCorpus Christi College University of Oxford  \nA thesis submitted for the degree of Doctor of Philosophy in Mathematics  \nMichaelmas 2024  \nAcknowledgements  \nFirst and foremost, I would like to thank my supervisor Prof. Harald Oberhauser for his ongoing support and guidance throughout my DPhil journey. I am deeply grateful to Harald for the thought-provoking conversations we had and for always supporting me in exploring my ideas. I would like to extend my gratitude to Prof. Terry Lyons and the DataSig team, who welcomed me as one of their own, and provided me with opportunities to present my work at various workshops and conferences. I would also like to thank the Mathematical Institute of the University of Oxford for generously providing me with a scholarship that allowed me to undertake this journey, and for providing the computational resources required for my applied projects.  \nI am grateful to my collaborators and colleagues for the many discussions we had: Patric Bonnier, Darrick Lee, Zoltán Szabó, Masaki Adachi, Patrick Kidger, Cristopher Salvi, Maud Lemercier, Christina Zou, Alexander Schell; thank you for your help and collegiality. I am also grateful to all my friends whether located in the UK or Hungary for supporting me in all ways and standing by me potentially despite the physical distance between us. Finally, I would like to thank the infinite support of my family: my sister Réka and my mother Éva; without your love and support I would not be where or who I am today. I dedicate this thesis to you.  \nDeclarations  \nThis thesis is submitted to the University of Oxford in support of my application for the degree of Doctor of Philosophy. It has been composed by myself under the supervision of Prof. Harald Oberhauser. I confirm that this thesis has not been submitted for another university degree. Parts of this thesis have appeared as published papers some of which were written with collaborators:  \n1. The work in Chapter 2 adapts the paper [266] written by me under the supervision of Harald Oberhauser published at the International Conference on Machine Learning in 2020 .  \n2. The work in Chapter 3 adapts the paper [263], that was written in collaboration with Patric Bonnier under the supervision of Harald Oberhauser published at the International Conference on Learning Representations in 2021 . In particular, I wrote the paper besides the theoretical results appearing originally in Appendices A, B and C, which were written by Patric, and due to space limitations these were omitted here and deferred to the article.  \n3. Chapter 4 adapts the paper [265] written in collaboration with Darrick Lee with frequent discussions with Celia Hacker and Harald Oberhauser published at the Advances in Neural Information Processing Systems in 2022 . My contribution was the idea of using expected signatures to describe random walks on graphs, deriving the governing equations both in the tensor-valued and low-rank case, implementing and running experiments, while Darrick formalized the theory and the connection to hypo-elliptic diffusions. The main text was written with equal contribution, while the parts of the appendix written by Darrick consisting of a background and certain theoretical proofs were deferred to the article.  \n4. Chapter 5 adapts the paper [267] published in SIAM Mathematics of Data Science in 2025 written by me with frequent discussions with Zoltán Szabó and Harald Oberhauser.  \n5. Chapter 6 adapts [262] which was published at Artificial Intelligence and Statistics in 2025 written by me with frequent discussions with Masaki Adachi and Harald Oberhauser.  \nAbstract  \nIn this thesis, we consider the integration of path signatures–a mathematical object rooted in rough path theory–with scalable machine learning algorithms to address challenges in sequential and structured data modelling. The key topics considered include:  \n• Path Signatures: In","cbCaiunaMyRjuAey","https://ap.wps.com/l/cbCaiunaMyRjuAey","pdf",4972148,1,209,"English","en",105,"# Introduction\n## Unifying theme\n## Outline","[{\"question\":\"What are the main methods studied in the thesis?\",\"answer\":\"The thesis studies path signature representations, their use with Gaussian processes, a Seq2Tens deep learning framework, and several scalable approaches such as random Fourier signature features and recurrent sparse spectrum signature Gaussian processes.\"},{\"question\":\"How does the thesis make path signatures scalable for large datasets?\",\"answer\":\"It addresses computational overhead using novel algorithms, sparse variational inference for Gaussian processes, low-rank layers in Seq2Tens, and random feature approximations for signature kernels.\"},{\"question\":\"How are path signatures extended to graph and time-series tasks?\",\"answer\":\"The work extends path signatures to graph data and links them to hypo-elliptic diffusions, using low-rank techniques for scalable architectures. For time-series forecasting and classification, it combines signature features with probabilistic modelling and random-feature approximations.\"}]","Scalable Machine Learning Algorithms using Path Signatures - Doctor of Philosophy Thesis | PDF",1785898207,527,{"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},"scalable-machine-learning-algorithms-using-path-signatures-doctor-of-philosophy-thesis","",{"@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/scalable-machine-learning-algorithms-using-path-signatures-doctor-of-philosophy-thesis/125329/",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","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What are the main methods studied in the thesis?","Question",{"text":75,"@type":76},"The thesis studies path signature representations, their use with Gaussian processes, a Seq2Tens deep learning framework, and several scalable approaches such as random Fourier signature features and recurrent sparse spectrum signature Gaussian processes.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the thesis make path signatures scalable for large datasets?",{"text":80,"@type":76},"It addresses computational overhead using novel algorithms, sparse variational inference for Gaussian processes, low-rank layers in Seq2Tens, and random feature approximations for signature kernels.",{"name":82,"@type":73,"acceptedAnswer":83},"How are path signatures extended to graph and time-series tasks?",{"text":84,"@type":76},"The work extends path signatures to graph data and links them to hypo-elliptic diffusions, using low-rank techniques for scalable architectures. 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