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Topics in Statistics: Statistical Learning Theory >> Content Detail



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

 








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