# TTIC 31120: Computational and Statistical Learning Theory

This is a web page for the Spring 2015 course "Computational and Statistical Learning Theory", taught at TTIC, and also open to all University of Chicago students.

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)
Familiarity with Convex Optimization, Computational Complexity and background in Statistics can be helpful, but is not required.

#### Specific Topics:

We will try to touch:
• 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
• 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
• Stability Based Analysis
• Boosting: Weak Learning and the Margin Interpretation of Boosting.

• Required Reading: Some material will be covered through assigned reading, rather than in-class.
• 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

We will not be following a specific text, but some of the material is covered in:

## Schedule and Lectures

Week of Monday Wednesday Friday
March 30th What is Learning?* PAC Learning and VC Theory I No class
April 6th PAC Learning and VC Theory II MDL and PAC-Bayes No class
April 13th No class Computational Complexity of Learning Proper vs Improper Learning
April 20th No class Hardness of Improper Learning
Agnostic Learning
Boosting
Compression Schemes
April 27th No class Real-Valued Loss Scale-Sensitive Classes
May 4th No class SVMs, L1 Regularization No class
May 11th No class L1 margin, Stability Online Learning
May 18th Online Gradient Descent No class Strong Convexity
Online Dual Averaging
May 25th No class Mirror Descent
Online to Batch
No class
June 1st Stochastic Optimization
Neural Networks
Course Summary
Nearest Neighbor Classificaiton
No class
June 8th Final Exam: Tuesday June 9, 10:30am

*The shaded slides are not required material.

## Assignments:

Problem Set 1 (due April 15th)
Problem Set 2 (due May 1st)
Problem Set 3+4 (due June 5th)