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 |