[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119328-en":3,"doc-seo-119328-105":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},119328,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",8,"Research & Report","Topics in Sparse Bayesian Machine Learning","This dissertation addresses challenging machine learning problems through Bayesian methodology, targeting settings common in epidemiology, biomedicine, robust statistics, and imaging science. The focus is on high-dimensional models under sparsity assumptions. Three core problems are studied: sparse canonical correlation analysis, minimum distance estimation, and inverse problems. For each problem, new Bayesian methods are proposed, providing statistical guarantees alongside computational and numerical evidence to support effective and efficient performance.","Boston University  \nOpenBU [http://open.bu.edu](http://open.bu.edu)  \n\n| Boston University Theses & Dissertations | Boston University Theses & Dissertations |\n| --- | --- |\n| 2023\u003Cbr>Topics in sparse | Bayesian machine learning |\n\n[https://hdl.handle.net/2144/49723](https://hdl.handle.net/2144/49723)  \n\"Downloaded from OpenBU. Boston University's institutional repository. \"  \nBOSTON UNIVERSITY  \nGRADUATE SCHOOL OF ARTS AND SCIENCES  \nDissertation  \nTOPICS IN SPARSE BAYESIAN MACHINE LEARNING  \nby  \nQIUYUN ZHU  \nB.S., Nanjing University, 2016  \nM.S., University of Wisconsin-Madison, 2017  \nSubmitted in partial ful􀀌llment of the requirements for the degree of  \nDoctor of Philosophy  \n􀀍c 2023 by QIUYUN ZHU All rights reserved  \nApproved by  \nFirst Reader  \nYves Atchad􀀓e, Ph.D.  \nProfessor of Mathematics and Statistics  \nSecond Reader  \nKonstantinos Spiliopoulos, Ph.D.  \nProfessor of Mathematics and Statistics  \nThird Reader  \nUri Eden, Ph.D.  \nProfessor of Mathematics and Statistics  \nFourth Reader  \nJonathan Huggins, Ph.D.  \nAssistant Professor of Mathematics and Statistics  \nAcknowledgments  \nI would like to 􀀌rst thank my advisor, Yves Atchad􀀓e. He encouraged me to pursue interesting and deep ideas, gave me absolute research freedom, and provided extremely valuable guidance in my research. I am very grateful for his generous guidance and support through my doctoral studies.  \nI thank Prof. Konstantinos Spiliopoulos, Prof. Uri Eden and Prof. Jonathan Huggins to serve on my thesis committee. Their constructive feedback helped me improve the thesis.  \nI am very fortunate to be a member of the department of mathematics and statistics, which is 􀀌lled with intelligent, generous, and sincere colleagues. I enjoyed the inspiring conversations with many of them.  \nI am also thankful to my amazing boyfriend, Renbo Zhao. His encouragement and support during the rough time of my research and life helped me to gain con􀀌dence and move on. I dedicate this thesis to him.  \nQiuyun Zhu  \nTOPICS IN SPARSE BAYESIAN MACHINE LEARNING  \nQIUYUN ZHU  \nBoston University, Graduate School of Arts and Sciences, 2023  \nMajor Professor: Yves Atchad􀀓e, PhD  \nProfessor of Mathematics and Statistics  \nABSTRACT  \nThis dissertation is devoted to addressing several challenging problems in machine learning via the Bayesian approach. These problems frequently arise in diverse 􀀌elds, such as epidemiology, biomedicine, robust statistics and imaging science, and are usually high-dimensional and have certain sparsity assumptions. In this dissertation, we will focus on three important problems, which are sparse canonical correlation analysis, minimum distance estimation and inverse problems. For each problem, we will develop a new method from the Bayesian perspective to solve it e􀀋ectively ande􀀎ciently, with statistical guarantees and numerical evidence.  \nContents  \n1 Introduction 1  \n2 Minimax quasi-Bayesian estimation in sparse canonical correlation analysis via a Rayleigh quotient function 4  \n2.1 Introduction ................................ 4  \n2.2 Quasi-Bayesian sparse CCA using a Rayleigh quotient function .... 7  \n2.2.1 A Quasi-Bayesian approach ................... 9  \n2.2.2 Connection with simulated annealing .............. 11  \n2.2.3 Rate of convergence ........................ 12  \n2.3 Computation using Markov Chain Monte Carlo ............ 16  \n2.3.1 Mixing times ........................... 16  \n2.4 Numerical studies ............................. 18  \n2.4.1 Simulated data generation .................... 19  \n2.4.2 Empirical studies of our algorithm ................ 19  \n2.4.3 Comparison with other methods ................. 22  \n2.5 Principal canonical correlation of clinical and proteomic data in Covid-  \n19 patients ................................. 27  \n2.6 Conclusion ................................. 31  \n3 A statistical perspective on algorithm unrolling models for inverse problems 32  \n3.1 Introduction ................................ 32  \n3.1.1 Learning ","cbCaidhoxmFw78FJ","https://ap.wps.com/l/cbCaidhoxmFw78FJ","pdf",1171420,1,144,"English","en",105,"# Contents\n## 1 Introduction\n## 2 Minimax quasi-Bayesian estimation in sparse canonical correlation analysis via a Rayleigh quotient function\n## 3 A statistical perspective on algorithm unrolling models for inverse problems\n## 4 Minimum Distance Estimation from the view of Game Theory\n## A Supplemental Materials to Chapter 2","[{\"question\":\"What scope does the dissertation cover in machine learning?\",\"answer\":\"It develops Bayesian approaches to several difficult machine learning problems that often occur in epidemiology, biomedicine, robust statistics, and imaging science.\"},{\"question\":\"Which three main research problems are emphasized?\",\"answer\":\"The dissertation focuses on sparse canonical correlation analysis, minimum distance estimation, and inverse problems.\"},{\"question\":\"What kinds of results and evidence does the dissertation provide for each method?\",\"answer\":\"For each problem, it develops a Bayesian method with statistical guarantees and numerical evidence, including computational approaches such as Markov Chain Monte Carlo where applicable.\"}]","Topics in Sparse Bayesian Machine Learning | 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