[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119503-en":3,"doc-seo-119503-105":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},119503,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","Mind the Metric - Methods in Metric-Informed Machine Learning","Various machine learning algorithms exploit metric structure in both data and model parameters to gain geometric priors. Such geometry can lower sample complexity, improve generalization, and help ensure feasibility of learned models. The dissertation develops metric-informed methods across probabilistic graphical models, reinforcement learning, and distributional sampling. It presents Riemannian geometry-aware approaches for quantum graphical models, geometry-aware sampling via kernel herding on non-Euclidean spaces, and state and policy representations using bisimulation-induced metric structure.","©Copyright 2025 Sandesh Adhikary  \nMind the Metric: Methods in Metric-Informed Machine Learning  \nSandesh Adhikary  \nA dissertation  \nsubmitted in partial fulfillment of the  \nrequirements for the degree of  \nDoctor of Philosophy  \nUniversity of Washington  \n2025  \nReading Committee:  \nByron Emereth Boots, Chair  \nAbhishekh Gupta  \nSewoong Oh  \nProgram Authorized to O↵er Degree:  \nComputer Science and Engineering  \nUniversity of Washington  \nAbstract  \nMind the Metric: Methods in Metric-Informed Machine Learning  \nSandesh Adhikary  \nChair of the Supervisory Committee:  \nByron Emereth Boots  \nComputer Science and Engineering  \nVarious machine learning algorithms can benefit from exploiting the metric structure inherent in data and model parameters. Such geometric structure can be a useful prior to reduce sample complexity, improve generalization, and ensure feasibility of learned models. We present a range of metric-informed machine learning methods that span probabilistic graphical models, reinforcement learning, and sampling from probability distributions.  \nWithin the domain of probabilistic graphical models, we use metric structure to learn feasible quantum-graphical models using geometry-aware optimization. Specifically, we present an approach to learn hidden quantum Markov models (HQMMs) through Riemannian gradient descent on the Stiefel manifold. Moreover, we establish a hierarchy of expressiveness relationships between HQMMs and linear sequential systems from various fields including machine learning, formal language, and quantum information.  \nWithin the domain of sampling based probabilistic inference, we use metric structure to define geometry-aware similarity measures for sampling in structured data spaces. Specifically, we adapt the kernel herding algorithm to non-Euclidean spaces using geometryaware kernels and Riemannian optimization. We demonstrate through empirical evaluations that Riemannian kernel herding outperforms various common heuristics and other geometryinformed approaches.  \nWithin the domain of reinforcement learning (RL), we use metric structure to define geometry-aware representations of states and policies. Specifically, we introduce Behavioral  \nEigenmaps (BeigeMaps)– state representations that preserve the local metric structure induced by bisimulation metrics through neural eigendecompositions of similarity kernels. When added as a drop-in modification, BeigeMaps improve the policy performance of prior behavioral distance-based RL algorithms by highlighting value-based clusters in state spaces. Moreover, we also introduce a framework for policy composition to aggregate policies learned in multi-objective RL as policy-centroids in distance spaces where policies are embedded.  \nACKNOWLEDGMENTS  \nThis dissertation would not have been possible without the academic and emotional support from family, friends, and colleagues. While any errors in this thesis are entirely my own, any positive progress made through this dissertation has been a collective e↵ort of all those who helped me through the process.  \nFirstly, I would like to thank my advisor Byron Boots, and my committee members including Sewoong Oh, Abhishek Gupta, and Yen-Chi Chen. I am grateful for the support they provided to shape this thesis into its ultimate form. I am particularly indebted to Byron for his guidance throughout my PhD. I first came across Byron and his work early in my PhD when I felt lost as a researcher. His encouragement and openness to exploring new ideas outside his comfort zone rejuvenated my interest in research. I deeply appreciate the confidence Byron placed in me to let me freely explore ideas from quantum information to robotics, with many enjoyable stops in between.  \nI would also like to thank the great research collaborators I have had the pleasure of working with throughout my PhD including Siddarth Srinivasan, Bibek Pokharel, Jacob Miller, Anqi Li, Jacob Sacks, Josie Thompson, Tyler Westenbroek, Chandra Bhagavatula, G","cbCaiiQExwfE5WCa","https://ap.wps.com/l/cbCaiiQExwfE5WCa","pdf",9149458,1,254,"English","en",105,"# Contents\n## Part I Introduction\n## 1 Methods in Metric Informed Machine Learning\n## 2 Metrics: Preliminaries\n## Part II Metric Informed Quantum Graphical Models\n## 3 Introduction","[{\"question\":\"How does metric structure help machine learning in this dissertation?\",\"answer\":\"Metric structure in data and model parameters provides geometric priors that can reduce sample complexity, improve generalization, and support feasibility of learned models.\"},{\"question\":\"What metric-informed methods are proposed for probabilistic graphical models?\",\"answer\":\"The work uses metric structure to learn feasible quantum-graphical models with geometry-aware optimization, including Riemannian gradient descent for hidden quantum Markov models and expressiveness relationships to linear sequential systems.\"},{\"question\":\"How are metric ideas applied to sampling and reinforcement learning?\",\"answer\":\"For sampling, metric structure defines geometry-aware similarity measures and adapts kernel herding to non-Euclidean spaces using geometry-aware kernels and Riemannian optimization. For reinforcement learning, the dissertation introduces BeigeMaps to preserve local metric structure via neural eigendecompositions and a policy-composition framework using policy-centroids in distance spaces.\"}]","Mind the Metric - Methods in Metric-Informed Machine Learning | PDF",1785724685,640,{"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},"mind-the-metric-methods-in-metric-informed-machine-learning","",{"@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/mind-the-metric-methods-in-metric-informed-machine-learning/119503/",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},"How does metric structure help machine learning in this dissertation?","Question",{"text":75,"@type":76},"Metric structure in data and model parameters provides geometric priors that can reduce sample complexity, improve generalization, and support feasibility of learned models.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What metric-informed methods are proposed for probabilistic graphical models?",{"text":80,"@type":76},"The work uses metric structure to learn feasible quantum-graphical models with geometry-aware optimization, including Riemannian gradient descent for hidden quantum Markov models and expressiveness relationships to linear sequential systems.",{"name":82,"@type":73,"acceptedAnswer":83},"How are metric ideas applied to sampling and reinforcement learning?",{"text":84,"@type":76},"For sampling, metric structure defines geometry-aware similarity measures and adapts kernel herding to non-Euclidean spaces using geometry-aware kernels and Riemannian optimization. For reinforcement learning, the dissertation introduces BeigeMaps to preserve local metric structure via neural eigendecompositions and a policy-composition framework using policy-centroids in distance spaces.","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"]