[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-128506-en":3,"doc-seo-128506-105":30,"detail-sidebar-cat-0-en-105":96},{"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},128506,687207017582,"Himbo","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Essays on Statistical Inference, Nonconvex Optimization and Machine Learning - Dissertation","The dissertation presents a set of research essays on statistical inference and optimization methods, with particular emphasis on nonconvex learning settings and practical algorithm design. It develops online bootstrap inference for nonconvex stochastic gradient descent, including covariance matrix estimation, moment bounds, and bootstrap confidence intervals supported by simulation examples and empirical experiments. It further proposes a conditional randomization rank test and studies its robustness and computational advantages, plus a zeroth-order expectation maximization algorithm to handle settings where gradient access may be limited.","Washington University in St. Louis  \nWashington University Open Scholarship  \n\n| Arts & Sciences Electronic Theses and\u003Cbr>Dissertations | Arts & Sciences |\n| --- | --- |\n| Spring 5-15-2023\u003Cbr>Essays on Statistical Inference, Nonconvex Optimization and Machine Learning\u003Cbr>Yanjie Zhong\u003Cbr>Follow this and additional works at: [https://openscholarship.wustl.edu/art_sci_etds](https://openscholarship.wustl.edu/art_sci_etds) |  |\n\nRecommended Citation  \nZhong, Yanjie, \"Essays on Statistical Inference, Nonconvex Optimization and Machine Learning\" (2023) . Arts & Sciences Electronic Theses and Dissertations. 2929.  \n[https://openscholarship.wustl.edu/art_sci_etds/2929](https://openscholarship.wustl.edu/art_sci_etds/2929)  \nThis Dissertation is brought to you for free and open access by the Arts & Sciences at Washington University Open Scholarship. It has been accepted for inclusion in Arts & Sciences Electronic Theses and Dissertations by an authorized administrator of Washington University Open Scholarship. For more information, please contact [digital@wumail.wustl.edu](digital@wumail.wustl.edu).  \nWASHINGTON UNIVERSITY IN ST.LOUIS  \nSchool of Art & Sciences  \nDepartment of Mathematics and Statistics  \nDissertation Examination Committee:  \nTodd Kuffner, Co-Chair  \nSoumendra Lahiri, Co-Chair  \nLikai Chen  \nRobert Lunde  \nAri Stern  \nEssays on Statistical Inference, Nonconvex Optimization and Machine Learning  \nby  \nYanjie Zhong  \nA dissertation presented to  \nWashington University in St. Louis  \nin partial fulfillment of the  \nrequirements for the degree  \nof Doctor of Philosophy  \nMay 2023  \nSt. Louis, Missouri  \n© 2023, Yanjie Zhong  \nTable of Contents  \nList [of Figures](of Figures........................................................................................... vi)[........................................................................................... vi](of Figures........................................................................................... vi)  \n[List of Tables](List of Tables ...........................................................................................)[ ...........................................................................................](List of Tables ...........................................................................................). x  \nAcknowledgments ...................................................................................... xii  \nAbstract ................................................................................................... xv  \nChapter 1: Introduction ............................................................................ 1  \n1.1 Online Bootstrap Inference with Nonconvex Stochastic Gradient Descent Estimator ........................................................................................ 2  \n1.2 Conditional Randomization Rank Test ................................................... 7  \n1.2.1 Related Work .......................................................................... 9  \n1.3 Zeroth-Order Expectation Maximization Algorithm .................................. 11  \n1.3.1 Related Work .......................................................................... 13  \nChapter 2: Online Bootstrap Inference with Nonconvex Stochastic Gradient Descent Estimator ................................................................................ 15  \n2.1 Notations and Global Assumptions ....................................................... 16  \n2.2 Preliminaries and Background .............................................................. 17  \n2.3 Bootstrap-Based Covariance Matrix Estimator ........................................ 20  \n2.3.1 Conditions and Setups .............................................................. 21  \n2.3.2 Moment Bounds on the Parameter Estimation Error ....................... 23  \n2.3.3 Bound on the Covariance Matrix Estimator .................................. 25  \n2.4 Bootstrap Confidence Interval ....","cbCaigMqvQr6Sqmz","https://ap.wps.com/l/cbCaigMqvQr6Sqmz","pdf",8477680,1,403,"English","en",105,"# Acknowledgments\n# Abstract\n# Chapter 1: Introduction\n## Online Bootstrap Inference with Nonconvex Stochastic Gradient Descent Estimator\n## Conditional Randomization Rank Test\n## Zeroth-Order Expectation Maximization Algorithm\n# Chapter 2: Online Bootstrap Inference with Nonconvex Stochastic Gradient Descent Estimator\n## Notations and Global Assumptions\n## Preliminaries and Background\n## Bootstrap-Based Covariance Matrix Estimator\n## Bootstrap Confidence Interval\n## Examples\n## Empirical Experiments\n## Discussion\n# Chapter 3: Conditional Randomization Rank Test\n## Notations\n## Conditional Randomization Rank Test\n## Robustness of the CRRT\n## Connections with Related Tests\n## Empirical Results\n## Discussions\n# Chapter 4: Zeroth-Order Expectation Maximization Algorithm","[{\"question\":\"What topics does the dissertation cover?\",\"answer\":\"It covers statistical inference and optimization methods, focusing on nonconvex stochastic gradient descent, conditional randomization rank testing, and a zeroth-order expectation maximization algorithm.\"},{\"question\":\"How does the work approach online bootstrap inference in nonconvex settings?\",\"answer\":\"It develops a bootstrap-based covariance matrix estimator, establishes moment and covariance bounds, and constructs bootstrap confidence intervals, then validates them with examples and empirical experiments.\"},{\"question\":\"What is the conditional randomization rank test (CRRT) and what are its advantages?\",\"answer\":\"The CRRT is presented as a rank-based testing method with studied robustness. The dissertation highlights connections to related tests and reports computational efficiency and improved performance in complicated settings.\"},{\"question\":\"What role does the zeroth-order expectation maximization algorithm play?\",\"answer\":\"It introduces an expectation-maximization approach using zeroth-order (gradient-free) information, with the chapter organized around definitions and algorithmic components for the targeted nonconvex inference/learning context.\"}]","Essays on Statistical Inference, Nonconvex Optimization and Machine Learning - Dissertation | PDF",1786001432,1016,{"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":91,"head_meta":93,"extra_data":95,"updated_unix":28},"essays-on-statistical-inference-nonconvex-optimization-and-machine-learning-dissertation","",{"@graph":36,"@context":90},[37,54,69],{"@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/essays-on-statistical-inference-nonconvex-optimization-and-machine-learning-dissertation/128506/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-22","2026-08-06",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82,86],{"name":73,"@type":74,"acceptedAnswer":75},"What topics does the dissertation cover?","Question",{"text":76,"@type":77},"It covers statistical inference and optimization methods, focusing on nonconvex stochastic gradient descent, conditional randomization rank testing, and a zeroth-order expectation maximization algorithm.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the work approach online bootstrap inference in nonconvex settings?",{"text":81,"@type":77},"It develops a bootstrap-based covariance matrix estimator, establishes moment and covariance bounds, and constructs bootstrap confidence intervals, then validates them with examples and empirical experiments.",{"name":83,"@type":74,"acceptedAnswer":84},"What is the conditional randomization rank test (CRRT) and what are its advantages?",{"text":85,"@type":77},"The CRRT is presented as a rank-based testing method with studied robustness. 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