ࡱ>   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry F=SummaryInformation(DocumentSummaryInformation8 WordDocumentt  Oh+'0   , 8DLT\IBMNormal\id_11@,EO@:@t=V=WPS Office_11.1.0.12598_F1E327BC-269C-435d-A152-05C5408002CA ՜.+,D՜.+,HPXlt| ؚSlQS ! 0t|KSOProductBuildVerICV2052-11.1.0.12598!EB73ED8ADDBF403F9EFA731D86CDC2070TableData WpsCustomData P8)KSKSt tm vB:V $ hO 8X T" mf  -NWS"~?el'Yf[ zYef['Y~ Course Syllabus of Zhongnan University of Economics and Law Course Title: High-Dimensional StatisticsCourse Code31133027Semester1Teaching Hours48Credits3Prerequisites HYPERLINK "javascript:;" Probability HYPERLINK "javascript:;" and HYPERLINK "javascript:;" Statistics,  HYPERLINK "javascript:;" Linear HYPERLINK "javascript:;" Regression, StatisticsInstructor InformationNameJing Zhang, Yuanshan WuEmail HYPERLINK "mailto:jing66@zuel.edu.cn" jing66@zuel.edu.cn  HYPERLINK "mailto:wu@zuel.edu.cn" wu@zuel.edu.cnInstituteSchool of Statistics and MathematicsApplicable ObjectInternational StudentsCourse ObjectivesThe course  High-Dimensional Statistics mainly introduces the basic concepts, basic theories and methods in high-dimensional statistics. It provides a self-contained introduction to the area of high-dimensional statistics. It includes chapters that are focused on core methodology and theory, as well as chapters devoted to in-depth exploration of particular model classes. Through the study of this course, it is hoped that students can master the basic theories and methods in high-dimensional statistics, and learn to use the knowledge to deal with high-dimensional data problems in practical applications. Course Description (200 words)Recent years have witnessed an explosion in the volume and variety of data collected in all scientific disciplines and industrial settings. Such massive data sets present a number of challenges to researchers in statistics and machine learning. This course provides a self-contained introduction to the area of high-dimensional statistics. It includes chapters that are focused on core methodology and theory, including tail bounds, concentration inequalities, uniform laws and empirical process, and random matrices; as well as chapters devoted to in-depth exploration of particular model classes, including sparse linear models, matrix models with rank constraints, graphical models, and various types of nonparametric models.Assessment Methods Course paper Textbooks and ReferencesWainwright, M. J. . (2019). High-Dimensional Statistics: A Non-Asymptotic Viewpoint. L. Bhlmann and Geer, S. . (2011).Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer. Course planningChapter 1Basic tail and concentration bounds 1.1 Classical bounds 1.2 Martingale-based methods 1.3 Lipschitz functions of Gaussian variables Chapter 2 Concentration of measure 2.1 Concentration by entropic techniques 2.2 A geometric perspective on concentration 2.3 Wasserstein distances and information inequalities 2.4 Tail bounds for empirical processesChapter 3Uniform laws of large numbers 3.1 Motivation 3.2 A uniform law via Rademacher complexity 3.3 Upper bounds on the Rademacher complexity Chapter 4Metric entropy and its uses 4.1 Covering and packing 4.2 Gaussian and Rademacher complexity 4.3 Metric entropy and sub-Gaussian processes 4.4 Some Gaussian comparison inequalities 4.5 Sudakov s lower bound 4.6 Chaining and Orlicz processesChapter 5Random matrices and covariance estimation 5.1 Some preliminaries 5.2 Wishart matrices and their behavior 5.3 Covariance matrices from sub-Gaussian ensembles 5.4 Bounds for general matrices 5.5 Bounds for structured covariance matricesChapter 6Sparse linear models in high dimensions 6.1 Problem formulation and applications 6.2 Recovery in the noiseless setting 6.3 Estimation in noisy settings 6.4 Bounds on prediction error 6.5 Variable or subset selectionChapter 7Principal component analysis in high dimensions 7.1 Principal components and dimension reduction 7.2 Bounds for generic eigenvectors 7.3 Sparse principal component analysis 7.4 Bibliographic details and backgroundChapter 8Decomposability and restricted strong convexity 8.1 A general regularized M-estimator 8.2 Decomposable regularizers and their utility 8.3 Restricted curvature conditions 8.4 Some general theorems 8.5 Bounds for sparse vector regression 8.6 Bounds for group-structured sparsity 8.7 Bounds for overlapping decomposition-based norms 8.8 Techniques for proving restricted strong convexity  ,.>DFVlƵyp_N=%.B*phCJo(aJ5KHmH sH nHtH\!CJo(aJ5mH sH nHtH\!CJo(aJ5mH sH nHtH\!CJo(aJ5mH sH nHtH\CJo(aJ5\!CJo(aJ5mH sH nHtH\!CJo(aJ5mH sH nHtH\!CJo(aJ5mH sH nHtH\CJo(aJ5\!CJo(aJ5mH sH nHtH\CJo(aJ5\CJOJPJQJ^Jo(aJ5CJOJPJQJ^Jo(aJ5B*phCJOJQJaJ5U    , . 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