[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117193-en":3,"doc-seo-117193-105":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},117193,4398048950312,"Violet","https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908",8,"Research & Report","Orthogonality in Machine Learning - Dissertation","This thesis examines how the concept of orthogonality, together with Hilbert-space perspectives, can be leveraged to strengthen existing machine learning algorithms and guide the creation of new ones. It develops applications grounded in orthogonal polynomials and demonstrates their value for feature construction. The work includes a sparse Gaussian process method with orthogonal basis functions, an interpretable feature construction for dynamic graphs using orthogonality between matching polynomials, and extensions based on Gaussian Cox processes that enable rapid Bayesian inference and uncertainty-quantified stochastic classification.","Orthogonality in Machine  \nLearning  \nWilliam Greenall  \nA dissertation submitted in partial fulfillment of the requirements for the degree of  \nDoctor of Philosophy  \nof  \nUniversity College London.  \nDepartment of Statistical Science University College London  \nJune 21, 2024  \n2  \nI, William Greenall, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I  \nconfirm that this has been indicated in the work.  \nAbstract  \nIn this thesis I focus on the applications and relevance of orthogonality in various topics in machine learning. The theme of the thesis is that different viewpoints of the concept of orthogonality and Hilbert spaces in general can be utilised to improve the performance of machine learning algorithms, as well as inform development of new ones. The approach taken focuses in part on the rich and interesting theory of orthogonal polynomials, which are heretofore underutilised in machine learning methods as a tool for feature construction  \nFirst, I look at a sparse Gaussian process schema relying on appropriate construction of orthogonal basis functions, as well as relevant theory that shows that orthonormality is an important feature of the chosen sparse method. This yields a novel approach to feature construction and sparse Gaussian process regression.  \nNext, I utilise orthogonality and an appropriately defined inner product as a tool for a new form of interpretable feature construction in problems with dynamic graphs. The approach centres on comparison between graphs via an implicit measure of orthogonality of their matching polynomials. This is applied to anomaly detection as a guiding example, using a ”landmarks” strategy.  \nFinally, I propose a new type of Gaussian Cox process, which yields application of orthogonal series estimate models in order to  \nAbstract 4  \nconstruct a rapid Bayesian inference scheme, bypassing the usual difficulties of the highly non-Gaussian likelihood. This is then extended, through appropriate approximation schemata for higher-order Gaussian moments, to stochastic classification models, yielding a rapid and flexible stochastic classifier, whose predictions can be interpreted as exact probabilities and yield direct uncertainty quantification. This stands in contrast to standard models that train on degenerate distributions to yield probabilistic predictions in an ad-hoc fashion.  \nImpact Statement  \nThe work in this thesis may have impact in both academic and industrial settings. The approach developed in the first chapter should improve predictive capability in any situation where Gaussian process models are used. This could be widespread, given that Gaussian process models are widely-used paradigm in general machine learning problems. The computational cost of methods translates directly to computing time, which has a cost both in financial and energy terms. As a result it is not easy to quantify ex ante the potential impact of the work in the first chapter. I expect to publish a paper based on the material in this chapter over the course of the next year at a top machine learning conference.  \nGraph-based methods have proliferated, and interpretability is a key concern in many of these models. The work in the second chapter should improve the interpretability of graph-based models, and so could have impact in any situation where such models are used. This could be widespread, given the increasing use of graph-based models in many areas of machine learning. Again, it is not easy to quantify ex ante the potential impact of the work in the second chapter. I also expect to find an appropriate venue for publication of a paper based on the material in this chapter over the course of the next year.  \nThe work in the third chapter is more directly applicable to a  \nImpact Statement 6  \nspecific industrial setting. Point process data is widespread in many areas, and the computational efficiency exhibited by the method may hav","cbCail9OtP8viNDi","https://ap.wps.com/l/cbCail9OtP8viNDi","pdf",6404602,1,188,"English","en",105,"# Abstract\n# Impact Statement\n# Acknowledgements\n# Notation","[{\"question\":\"How does the thesis use orthogonality and Hilbert spaces in machine learning?\",\"answer\":\"It treats different viewpoints of orthogonality and Hilbert spaces as tools to improve algorithm performance and to inform the design of new methods.\"},{\"question\":\"What role do orthogonal polynomials play in the proposed approaches?\",\"answer\":\"Orthogonal polynomials are used as an underutilized theoretical foundation to enable feature construction across multiple machine learning settings described in the thesis.\"},{\"question\":\"How is interpretable feature construction achieved for dynamic graphs?\",\"answer\":\"The thesis defines an inner-product-based notion of orthogonality to compare graphs via their matching polynomials, and applies this framework to anomaly detection using a landmarks strategy.\"}]","Orthogonality in Machine Learning - Dissertation | PDF",1785674356,474,{"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},"orthogonality-in-machine-learning-dissertation","",{"@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/orthogonality-in-machine-learning-dissertation/117193/",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","2026-08-02",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},"How does the thesis use orthogonality and Hilbert spaces in machine learning?","Question",{"text":75,"@type":76},"It treats different viewpoints of orthogonality and Hilbert spaces as tools to improve algorithm performance and to inform the design of new methods.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What role do orthogonal polynomials play in the proposed approaches?",{"text":80,"@type":76},"Orthogonal polynomials are used as an underutilized theoretical foundation to enable feature construction across multiple machine learning settings described in the thesis.",{"name":82,"@type":73,"acceptedAnswer":83},"How is interpretable feature construction achieved for dynamic graphs?",{"text":84,"@type":76},"The thesis defines an inner-product-based notion of orthogonality to compare graphs via their matching polynomials, and applies this framework to anomaly detection using a landmarks strategy.","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"]