CSC 665 Section 2: Machine Learning Theory - Fall 2019

Tentative schedule:

Date Topics Notes Additional Readings Homework
Aug 27 Introduction, motivation, course mechanics slides probability review SSBD App B.1 and B.2 HW0
Aug 29 Concentration of measure concentration of measure note 1 SSBD App B.4
Sep 3 Chernoff bound for Bernoulli random variables, McDiarmid’s Inequality concentration of measure note 2 SSBD App B.3, Lemma 26.4 HW0 due in class
Sep 5 The PAC learning framework, finite classes PAC learning note SSBD Chap 2, Sec 3.1
Sep 10 Agnostic PAC learning, infinite classes SSBD Sec 3.2-3.3, Chap 4, Sec 6.1
Sep 12 VC Theory, Sauer’s Lemma VC Theory note SSBD Sec 6.2 - 6.5.1
Sep 17 Rademacher complexity Uniform convergence / Rademacher complexity note SSBD Sec 6.5.2, 26.1, 28.1 HW1
Sep 19 Information-theoretic lower bounds of PAC learning SSBD 28.2.1
Sep 24 Le Cam’s method SSBD 28.2.1
Sep 26 Assouad’s method, fundamental theorem of statistical learning Lower bound note SSBD Sec 28.2.2, Sec 5.1 HW2
Oct 1 Support Vector Machine (SVM); the maximum margin hyperplane problem SSBD Chap 15, Secs 26.2, 26.3
Oct 3 Soft margin, nonlinear mapping, the dual of SVM SSBD Sec 15.4
Oct 8 Kernel trick SSBD Chap 16
Oct 10 Margin bounds, generalization bounds of SVM SSBD Sec 26.3
Oct 15 Proof of margin bounds via Rademacher complexity SVM note SSBD Secs 26.2, 26.4
Oct 17 Model selection, structural risk minimization Model selection note SSBD Chap 7, Modern bias-variance tradeoff Midterm (take home)
Oct 22 Boosting: AdaBoost SSBD Chap 10
Oct 24 Boosting and margin bound; two styles of margin bounds Boosting note SSBD Sec 26.2, Boosted ResNet paper
Oct 29 Intro to Online learning; Online classification SSBD Sec 21.1 HW3
Oct 31 Minimax analysis: Littlestone’s dimension; Expert problem Online classification note SSBD Sec 21.1.1
Nov 5 Cover’s Impossibility Result; Decision-theoretic online learning. Handwritten notes SSBD Sec 21.2
Nov 7 Hedge; Online to Batch conversion. Online to batch conversion notes SSBD Sec 21.2.1, Hedge paper; Loss range adaptivity
Nov 12 Convexity, subgradients SSBD Sec 12.1, 14.2
Nov 14 Bregman divergence, norms, dual norms
Nov 19 Lipschitzness, strong convexity and smoothness SSBD Sec 12.1, 13.3 HW4
Nov 21 Legendre-Fenchel conjugacy, online convex optimization, Follow the regularized leader (FTRL) OCO note Section 2.7, 2.3 of Shalev-Shwartz’s Survey
Nov 26 Analysis of FTRL; FTRL Examples H Sec 5.3
Nov 28 No Class. Thanksgiving Holiday!
Dec 3 Online linear classification with margins; FTRL with Adaptive regularization Section 3.3 of Shalev-Shwartz’s Survey; H Sec 5.6
Dec 5 Adagrad, online optimization of strongly convex functions H Sec 3.3
Dec 10 Final presentation Topics to review