Learning Theory

CS395T, Fall 2011
BUR 212, Mon & Wed 2:00 - 3:30 pm

Instructors Adam Klivans and Pradeep Ravikumar
TA Yi-Chao Chen

Office Hours Yi-Chao Chen (TA): TA Station 5, PAI 5.33, Thursdays 1:00 - 4:00 pm

Pradeep Ravikumar: ACES 2.434, Fridays 3:30-5:00 pm
Adam Klivans: TBD

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/Papers Statistical Learning Theory:
All of Statistics. Larry Wasserman.
The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Trevor Hastie, Robert Tibshirani, Jerome Friedman.
A Probabilistic Theory of Pattern Recognition. Luc Devroye, Laszlo Györfi, Gabor Lugosi.

Comp. Learning Theory:
An Introduction to Computational Learning Theory. Michael Kearns, Umesh Vazirani.

Background on Probability and Statistics:
Introduction to Probability and Statistics. Dimitri P. Bertsekas and John N. Tsitsiklis.
Statistical Inference. George Casella, Roger L. Berger.

Graphical Models:
Graphical models, exponential families, and variational inference. M. J. Wainwright and M. I. Jordan. Foundations and Trends in Machine Learning, Vol. 1, Numbers 1--2, pp. 1--305, December 2008.
Probabilistic Graphical Models: Principles and Techniques. D. Koller and N. Friedman.

High-dimensional Statistics:
Sharp thresholds for noisy and high-dimensional recovery of sparsity using $\ell_1$-constrained quadratic programming (Lasso). M. J. Wainwright. IEEE Transactions on Information Theory, 55:2183--2202, May 2009.
Paper: A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers. S. Negahban, P. Ravikumar, M. J. Wainwright and B. Yu, 2010.

  • Homework 1 is out. Due Oct 10, 2010.

Module Date Topic Notes Faculty
1: Statistical Models

Comptastical Thinking

Exponential Families, Generalized Linear Models

Scribe Notes PR
Statistical Models for Ranking

Scribe Notes Ambuj Tewari
2: Graphical Models

Graphical Models : Introduction

Scribe Notes PR
Graphical Models : Inference I (Variable Elimination, Sum-product)

Scribe Notes PR
Graphical Models : Inference II (Junction Trees)

Graphical Models : Inference/Learning as Optimization I

Scribe Notes PR
Graphical Models : Inference/Learning as Optimization II

3: High-dimensional Models

High-dimensional Statistics: Introduction (Sparsity, Group-Sparsity, Low-Rank)

Slides PR
High-dimensional Statistical Analysis (Sparsistency, Parameter Error Bounds)

Slides PR
4: Risk Bounds

ERM, {Estimation, Approximation} Error

DGL; Chapter 12 AT
Uniform Deviation Bounds, Glivenko-Cantelli Theorem

DGL; Chapter 12 AT
Glivenko-Cantelli Theorem (contd.), VC Theorem

DGL; Chapter 12 AT