| 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 |
