LEC # | TOPICS |
---|---|

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 |

## Calendar

## Course Info

##### Topics

##### Learning Resource Types

*notes*Lecture Notes

*assignment*Problem Sets