Learning Theory

CS395T, Fall 2010
BEN 1.126, Tues & Thurs 2:00 - 3:30 pm

Instructors Adam Klivans and Pradeep Ravikumar

Office Hours ACES 2.434, Mondays 3:30-5:00 pm (by appointment)
Overview A central problem in machine learning is to develop algorithms that have provable guarantees in terms of both running time and number of "training" observations required. Computational Learning Theory has traditionally focused on the first issue (the computational complexity of learning algorithms) while Statistical Learning Theory has focused on the second (their statistical efficiency). In this course we will cover both these aspects, and try to understand how learning is constrained given limited computation and limited data.

Grading Four problem sets (3/4 of final grade), and a final paper presentation (1/4 of final grade).

(Optional) Textbooks An Introduction to Computational Learning Theory. Michael Kearns, Umesh Vazirani
A Probabilistic Theory of Pattern Recognition. Luc Devroye, Laszlo Györfi, Gabor Lugosi.
The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Trevor Hastie, Robert Tibshirani, Jerome Friedman.

(Tentative) Schedule
Module Date Topic Notes Faculty
1,2 ... ... AK
... ... AK
Fourier Learning Papers: [1] [2] [3] Guest Lect: Homin Lee
3: Statistical Analysis Foundations

(2 weeks). Consistency, Convergence Rates, Generalization Error.
Useful Inequalities DGL; Chapter 8 PR
Glivenko-Cantelli Theorem DGL; Chapter 12 PR
V-C Theorem DGL; Chapter 12 PR
4: Complexity of Learning

(2 weeks). VC Theory, Metric Entropy, Rademacher Complexity, Margin Bounds.
Shatter Coefficients, V-C Dimension DGL; Chapter 13 PR
Metric Entropy DGL; Chapter 28 PR
Uniform Deviations of Averages from Expectations DGL; Chapter 29 PR
Rademacher Complexity Guest Lect: Ambuj Tewari
5: Misc

Surrogate Losses for Classification Paper: [1] PR
Reproducing Kernel Hilbert Spaces Book: [1] PR