| 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 |
