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Last updated:

September 23, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

The main goal of this course is to study the generalization ability of a number of popular

machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.

Course Curriculum

  • Voting classifiers, training error of boosting Unlimited
  • Support vector machines (SVM) Unlimited
  • Generalization error of SVM Unlimited
  • One dimensional concentration inequalities. Bennett’s inequality Unlimited
  • Bernstein’s inequality Unlimited
  • Hoeffding, Hoeffding-Chernoff, and Khinchine inequality Unlimited
  • Vapnik-Chervonenkis classes of sets Unlimited
  • Properties of VC classes of sets Unlimited
  • Symmetrization. Pessimistic VC inequality Unlimited
  • Optimistic VC inequality Unlimited
  • VC subgraph classes of functions. Packing and covering numbers Unlimited
  • Covering numbers of the VC subgraph classes Unlimited
  • More symmetrization. Generalized VC inequality Unlimited
  • Consequences of the generalized VC inequality Unlimited
  • Covering numbers of the convex hull Unlimited
  • Uniform entropy condition of VC-hull classes Unlimited
  • Generalization error bound for VC-hull classes Unlimited
  • Bounds on the generalization error of voting classifiers Unlimited
  • Bounds on the generalization error of voting classifiers (cont.) Unlimited
  • Bounds on the generalization error of voting classifiers (cont.) Unlimited
  • Bounds in terms of sparsity Unlimited
  • Bounds in terms of sparsity (cont.) (example) Unlimited
  • Martingale-difference inequalities Unlimited
  • Comparison inequality for Rademacher processes Unlimited
  • Application of martingale inequalities. Generalized martingale inequalities Unlimited
  • Generalization bounds for neural networks Unlimited
  • Generalization bounds for neural networks (cont.) Unlimited
  • Generalization bounds for kernel methods Unlimited
  • Optimistic VC inequality for random classes of sets Unlimited
  • Applications of random VC inequality to voting algorithms and SVM Unlimited
  • Talagrand’s convex-hull distance inequality Unlimited
  • Consequences of Talagrand’s convex-hull distance inequality Unlimited
  • Talagrand’s concentration inequality for empirical processes Unlimited
  • Talagrand’s two-point inequality Unlimited
  • Talagrand’s concentration inequality for empirical processes Unlimited
  • Applications of Talagrand’s concentration inequality Unlimited
  • Applications of talagrand’s convex-hull distance inequality. Bin packing Unlimited
  • Entropy tensorization inequality. Tensorization of Laplace transform Unlimited
  • Application of the entropy tensorization technique Unlimited
  • Stein’s method for concentration inequalities Unlimited

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Massachusetts Institute of Technology
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