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Browse materialsMIT 18.465 · Spring 2007

Topics in Statistics: Statistical Learning Theory

Subjects: Artificial Intelligence · Mathematics · Science · Statistics

Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain

Instructor: Prof. Dmitry Panchenko
Term: Spring 2007
Level: Graduate
What's inside: 2 problem sets · 1 lecture note · 1 reading · 76 other files · 3 web pages
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Source: MIT OpenCourseWare 18.465 Topics in Statistics: Statistical Learning Theory, Spring 2007, Prof. Dmitry Panchenko — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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MIT OpenCourseWare, Prof. Dmitry Panchenko, 18.465 Topics in Statistics: Statistical Learning Theory, Spring 2007.

License: CC BY-NC-SA 4.0 · Edition: Spring 2007 · Open the original course on OCW ↗

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Topics in Statistics: Statistical Learning Theory

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Other materials from this course

Lecture 1: Introduction

Lecture 2: Voting classifiers, training error of boosting

Lecture 3: Support vector machines (SVM)

Lecture 4: Generalization error of SVM

Lecture 5: One dimensional concentration inequalities. Bennett’s inequality

Lecture 6: Bernstein’s inequality

Lecture 7: Hoeffding, Hoeffding-Chernoff, and Khinchine inequality

Lecture 8: Vapnik-Chervonenkis classes of sets

Lecture 9: Properties of VC classes of sets

Lecture 10: Symmetrization. Pessimistic VC inequality

Lecture 11: Optimistic VC inequality

Lecture 12: VC subgraph classes of functions. Packing and covering numbers

Lecture 13: Covering numbers of the VC subgraph classes

Lecture 14: Kolmogorov’s chaining method. Dudley’s entropy integral

Lecture 15: More symmetrization. Generalized VC inequality

Lecture 16: Consequences of the generalized VC inequality

Lecture 17: Covering numbers of the convex hull

Lecture 18: Uniform entropy condition of VC-hull classes

Lecture 19: Generalization error bound for VC-hull classes

Lecture 20: Bounds on the generalization error of voting classifiers

Lecture 21: Bounds on the generalization error of voting classifiers (cont.)

Lecture 22: Bounds on the generalization error of voting classifiers (cont.)

Lecture 23: Bounds in terms of sparsity

Lecture 24: Bounds in terms of sparsity (cont.) (example)

Lecture 25: Martingale-difference inequalities

Lecture 26: Comparison inequality for Rademacher processes

Lecture 27: Application of martingale inequalities. Generalized martingale inequalities

Lecture 28: Generalization bounds for neural networks

Lecture 29: Generalization bounds for neural networks (cont.)

Lecture 30: Generalization bounds for kernel methods

Lecture 31: Optimistic VC inequality for random classes of sets

Lecture 32: Applications of random VC inequality to voting algorithms and SVM

Lecture 33: Talagrand’s convex-hull distance inequality

Lecture 34: Consequences of Talagrand’s convex-hull distance inequality

Lecture 35: Talagrand’s concentration inequality for empirical processes

Lecture 36: Talagrand’s two-point inequality

Lecture 37: Talagrand’s concentration inequality for empirical processes

Lecture 38: Applications of Talagrand’s concentration inequality

Lecture 39: Applications of talagrand’s convex-hull distance inequality. Bin packing

Lecture 40: Entropy tensorization inequality. Tensorization of Laplace transform

Lecture 41: Application of the entropy tensorization technique

Lecture 42: Stein’s method for concentration inequalities