时间：2019年6月24-25日
地点：中北校区理科大楼A1514会议室
题目：Introduction to Nonasymnptotic Statistical Analysis
授课老师：Prof. Yiyuan She, Florida State University
课程介绍与要求：
The short course involves some theoretic topics in statistics and machine learning. By the end of the course, students will acquire a basic understanding of some nonasymptotic statistical tools in concentration inequalities and empirical processes. This course is expected to be research-oriented and theoretical.
Prerequisite includes basic statistics and probability knowledge. Some basic knowledge in machine learning and optimization would be helpful.
9:00-11:30，June 24
Chernoff’s bounding, subGaussian random variables, Hoeffding’s inequality, Bernstein’s inequality, subexponential random variables, Bernstein’s moment growth condition, Johnson-Lindenstrauss Lemma, McDiarmid's inequality, the martingale method, Gaussian concentration, Talagrand concentration inequality
13:30-16:00，June 24
Entropy method, Herbst's argument, log-Sobolev inequalities, Glivenko-Cantelli theorem, empirical risk minimization, Rademacher complexity and empirical Rademacher complexity, symmetrization, contraction inequalities, Massart's finite-class lemma, growth function, VC dimension, Sauer's lemma
9:00-11:30, June 25
covering, packing, metric entropy, the volume argument, sub-Gaussian processes, Dudley's entropy integral, chaining, Haussler's bound, Sudakov's minoration inequality, Orlicz norms, random entropy condition, entropy with bracketing, uniform entropy, Donsker classes Regression, L0-constrained regression
13:30-16:00, June 25
sparse regression, nonconvex penalties, oracle inequalities, regularity conditions, M-estimators, U-statistics, nonparametric regression, localization, classification, PAC learning, empirical risk minimization, margin loss, hinge loss, support vector machines