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The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting
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3
English
English [CC]
FREE
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Description
support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.
Course content
- 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
- Kolmogorov’s chaining method. Dudley’s entropy integral 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
Instructor
Massachusetts Institute of Technology
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