TTIC 31120: Computational and Statistical Learning Theory

MWF 10:30-11:50AM in TTIC 530 (some of the classes will be canceled. Please see the schedule at the bottom of the page.)
Instructor: Nati Srebro.
TA: Behnam Neyshabur.

Course Description

The purpose of this course is to gain a deeper understanding of machine learning by formalizing learning mathematically, studying both statistical and computational aspects of learning, and understanding how these two aspects are inseparable. The course is intended both for students interested in using machine learning methods and that would like to understand such methods better so as to use them more effectively, as well as for students interested in the mathematical aspects of learning or that intend on rigorously studying or developing learning algorithms.

We will discuss classic results and recent advances in statistical learning theory (mostly under the agnostic PAC model), touch on computational learning theory, and also explore the relationship with stochastic optimization and online regret analysis. Our emphasis will be on concept development and on obtaining a rigorous quantitative understanding of machine learning. We will also study techniques for analyzing and proving performance guarantees for learning methods.

Prerequisites

• Mathematical maturity, as obtain, e.g., in a rigorous analysis course.
• Discrete Math (specifically combinatorics and asymptotic notation)
• Probability Theory
• Introduction to Machine Learning
• Algorithms; Basic Complexity Theory (NP-Hardness)

Specific Topics:

• The Statistical Model (Learning Based on an IID Sample):
  • The PAC (Probably Approximately Correct) and Agnostic PAC models.
  • Stochastic Optimization
  • Cardinality Bounds
  • Description Length Bounds
  • PAC-Bayes
  • Compression Bounds
  • The Growth Function and VC Dimension
  • VC Subgraph Dimension and Fat Shattering Dimension
  • Tight Characterization of Learning in terms of the VC and Fat Shattering Dimensions
  • Covering Numbers
  • Rademacher Averages, including Local Rademacher Analysis
• Uniform Learning and No-Free Lunch Theorems
• Online Learning, Online Optimization and Online Regret
  • The Perceptron Rule and Online Gradient Descent
  • Experts and the Winnow Rule
  • Bregman Divergence and Online Mirror Descent
  • Online to Batch Conversion
• Computational Lower Bounds:
  • Computational Hardness of Proper Learning
  • Cryptographic Hardness of Learning
• Additional Topics
  • Stability Based Analysis
  • Boosting: Weak Learning and the Margin Interpretation of Boosting.

Requirements and Grading:

• Required Reading: Some material will be covered through assigned reading, rather than in-class.
• Grading: Your grade will be based on the final exam and homeworks (they contribute equally to the final grade).
  • Problem Sets: About 4-5 problem sets, some of which introducing additional material beyond the material covered in class. Some problem sets will also include optional extra-credit problems.
  • Final Exam: The final exam will mostly consist of claims where you will be required to either affirm the claim is true (without providing a proof), or provide a counterexample to the claim.

Recommended Texts

• Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, 2014.
• O. Bousquet, S. Boucheron, and G. Lugosi. "Introduction to statistical learning theory." Advanced Lectures on Machine Learning, pp. 169-207. Springer Berlin Heidelberg, 2004.
• Michael J. Kearns and Umesh Virkumar Vazirani. An Introduction to Computational Learning Theory. MIT Press, 1994.

Schedule and Lectures

Assignments: