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Topics in Statistics: Statistical Learning Theory >> Content Detail



Lecture Notes



Lecture Notes

The lecture notes for this course were prepared by Alexander Rakhlin and Wen Dong, students in the class.

Complete set of lecture notes in one file (PDF - 4.8 MB)


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

 








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