[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117381-en":3,"doc-seo-117381-105":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},117381,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Kernel Methods - Generalisations, Scalability and Towards the Future of Machine Learning","Kernel methods form a broad family of machine learning algorithms popularized by Gaussian processes and support vector machines, but they also encompass decision trees, neural networks, determinantal point processes, and Gauss Markov random fields. The thesis advances three contributions: generalization, scalability, and future directions. It links diverse learning methods through kernel viewpoints, introduces a constrained kernel regression formulation for statistical parity in expectation to support group fairness, and shows efficient incorporation into deployed models. It further develops stochastic trace estimation improvements, Bayesian and entropic inference for log-determinants, and explores quantum-inspired approaches for Gaussian processes to achieve polylogarithmic-time linear algebra routines.","Kernel Methods: Generalisations, Scalability and Towards the Future of  \nMachine Learning  \nJack Fitzsimons The Queen’s College University of Oxford  \nA thesis submitted for the degree of Doctor of Philosophy  \nHilary 2019  \n2  \nAcknowledgements  \nI would first like to thank my supervisors Prof Michael Osborne and Prof Stephen Roberts for their belief in me and continued support. They have not only shown a great deal of patience but have also provided an environment in which I have been able to develop as an independent researcher with the necessary support along the way. I am confident that their roles in my graduate education will stand to me for many years to come.  \nThis work would also not have been possible without the strong collaborators I’ve had over the past few years, such as: Prof Maurizio Filippone, Prof Joseph Fitzsimons, Dr Zhikuan Zhao, Kurt Cutajar and Diego Granziol. Their insightful conversations and enthusiasm led to each of the publications at the core of this thesis.  \nOf course, not all conversations and inspired moments translate into published work. I am deeply indebted to all the members of the Machine Learning Research Group at the University of Oxford for the numerous brainstorms at whiteboards, thought-provoking discussions at the Crown Victoria and social outings. A special thank you goes to Dr Steve Reece, Jonathan Downing, Logan Graham, Dr Justin Bewsher, Dr Ibrahim Almosallam, Dr Tom Nickson, Dr Elmarie van Heerden, Rory Beard, Dr Tom Gunter, Dr Chris Llyod, Dr Tom Rainforth, Gabriele Abbati, Dr Glen Calopy, Dr Ali Syed Rizvi and Dr Favour Nyikosa.  \nFinally and most importantly, I am forever thankful to my family, especially tomy parents. They have not only supported me through my graduate education but have shown my siblings and I the importance of education and hard work since a  \nyoung age. They have acted as great role models to us all.  \nViva Examiners  \nI would like to formally thank my viva examiners,  \nProf Carl Rasmussen, Machine Learning Group, Department of Engineering, University of Cambridge.  \nDr Jan-Peter Calleiss, Machine Learning Research Group, Oxford-Man Institute for Quantitative Finance, University of Oxford.  \nfor their interesting discussion, insightful comments and advice for future research. I hope to carry their advice and comments with me in my future research endeavours.  \nAbstract  \nKernel methods are a broad class of machine learning algorithms made popular by Gaussian processes and support vector machines. Other popular methods, less commonly referred to as kernel methods, are decision trees, neural networks, determinantal point processes and Gauss Markov random fields.  \nThere are three core areas of contribution in this thesis, namely the generalization, scalability and future of kernel methods.  \nThe work begins by introducing kernel methods from the viewpoint of regression and classification, identifying the links between a myriad of machine learning algorithms. This general perspective of kernel methods is leveraged to address an important question faced by our field; how do we develop machine learning techniques which constrains inference as to maintain equality in expectation of the predictor. This has application to an open problem in algorithmic fairness referred to as Group Fairness, that is to do not suffer from group level inequalities. To answer this, a novel definition for statistical parity (group fairness in expectation) is introduced and is shown to have a natural form as constrained kernel regression. A key feature of this fairness constraint is that it can easily be incorporated into many widespread models in production without the requirement of retraining. It also deals with issues such as intersectionality and is applied to synthetic data, salary predictions of civil servants in the state of Illinois and the ProPublica dataset.  \nScalability is the second core focus of the work. Kernel methods are often un-  \nable tobe solved for in closed form wh","cbCaisnjlH9rY1g7","https://ap.wps.com/l/cbCaisnjlH9rY1g7","pdf",2988494,1,181,"English","en",105,"# Contents\n## I Machine Learning: The State of Affairs\n## 1 Introduction\n## II Kernel Methods as a Way of Life\n## 2 Fitting Lines","[{\"question\":\"What are the main research contributions of the thesis?\",\"answer\":\"The thesis focuses on three core areas: generalisation, scalability, and future directions for kernel methods.\"},{\"question\":\"How does the thesis address group fairness in kernel methods?\",\"answer\":\"It introduces a novel definition of statistical parity in expectation and shows it can be expressed as constrained kernel regression, enabling fairness constraints to be incorporated into many production models without retraining.\"},{\"question\":\"What scalability techniques are developed in the thesis?\",\"answer\":\"It thoroughly explores stochastic trace estimation by proposing a technique for sampling probe vectors, and it also develops Bayesian and entropic approaches to infer key linear algebra quantities such as log-determinants.\"}]","Kernel Methods - 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