Topics in Statistics: Statistical Learning Theory

Calendar

LEC #	TOPICS
1	Introduction
2	Voting classifiers, training error of boosting
3	Support vector machines (SVM)
4	Generalization error of SVM
5	One dimensional concentration inequalities. Bennett’s inequality
6	Bernstein’s inequality
7	Hoeffding, Hoeffding-Chernoff, and Khinchine inequality
8	Vapnik-Chervonenkis classes of sets
9	Properties of VC classes of sets
10	Symmetrization. Pessimistic VC inequality
11	Optimistic VC inequality
12	VC subgraph classes of functions. Packing and covering numbers
13	Covering numbers of the VC subgraph classes
14	Kolmogorov’s chaining method. Dudley’s entropy integral
15	More symmetrization. Generalized VC inequality
16	Consequences of the generalized VC inequality
17	Covering numbers of the convex hull
18	Uniform entropy condition of VC-hull classes
19	Generalization error bound for VC-hull classes
20	Bounds on the generalization error of voting classifiers
21	Bounds on the generalization error of voting classifiers (cont.)
22	Bounds on the generalization error of voting classifiers (cont.)
23	Bounds in terms of sparsity
24	Bounds in terms of sparsity (cont.) (example)
25	Martingale-difference inequalities
26	Comparison inequality for Rademacher processes
27	Application of martingale inequalities. Generalized martingale inequalities
28	Generalization bounds for neural networks
29	Generalization bounds for neural networks (cont.)
30	Generalization bounds for kernel methods
31	Optimistic VC inequality for random classes of sets
32	Applications of random VC inequality to voting algorithms and SVM
33	Talagrand’s convex-hull distance inequality
34	Consequences of Talagrand’s convex-hull distance inequality
35	Talagrand’s concentration inequality for empirical processes
36	Talagrand’s two-point inequality
37	Talagrand’s concentration inequality for empirical processes
38	Applications of Talagrand’s concentration inequality
39	Applications of talagrand’s convex-hull distance inequality. Bin packing
40	Entropy tensorization inequality. Tensorization of Laplace transform
41	Application of the entropy tensorization technique
42	Stein’s method for concentration inequalities