PENN CIS 6250, FALL 2023: THEORY OF MACHINE LEARNING

PENN CIS 6250, FALL 2023: THEORY OF MACHINE LEARNING

Prof. Michael Kearns
mkearns@cis.upenn.edu

Time: Tuesdays and Thursdays 10:15-11:45
Location: MacNeil 286-7
Attendance at lectures is a course requirement.
MK Office Hours: Right after class on Thursdays or by appointment. Weather permitting, I'll hold OHs in the outdoor seating area near MacNeil, otherwise in one of my offices. Please let me know in advance if you intend to come to OHs.

Teaching Assistants:
Brian Lee: wblee@wharton.upenn.edu
Office Hours: Tuesdays 12-1:30 in the Levine 4th floor bump space.
Keshav Ramji: keshavr@seas.upenn.edu
Office Hours: Wednesdays 5-6:30 in 612 Levine.

URL for this page:
www.cis.upenn.edu/~mkearns/teaching/CIS625

COURSE DESCRIPTION

This course is an introduction to the theory of machine learning, and provides mathematical, algorithmic, complexity-theoretic and probabilistic/statistical foundations to modern machine learning and related topics.

The first part of the course will follow portions of An Introduction to Computational Learning Theory, by M. Kearns and U. Vazirani (MIT Press). We will cover perhaps 6 or 7 of the chapters in K&V over (approximately) the first half of the course, often supplementing with additional readings and materials. I will provide electronic versions of the relevant chapters of K&V.

The second portion of the course will focus on a number of models and topics in learning theory and related areas not covered in K&V.

The course will give a broad overview of the kinds of theoretical problems and techniques typically studied and used in machine learning, and provide a basic arsenal of powerful mathematical tools for analyzing machine learning problems.

Topics likely to be covered include:

Basics of the Probably Approximately Correct (PAC) Learning Model

Occam's Razor, Compression and Learning

Concentration, Uniform Convergence and the Vapnik-Chervonenkis Dimension

Boosting and Related Techniques

Learning in the Presence of Noise and Statistical Query Learning

Learning and Cryptography

Query Models

Online and No-Regret Learning Models

Agnostic Learning

Game Theory and Machine Learning

Learning and Differential Privacy

Fairness in Machine Learning

Theory of Reinforcement Learning

COURSE FORMAT, REQUIREMENTS, AND PREREQUISITES

The lectures will be in a mixture of "chalk talk" format and markup of lecture notes, but with ample opportunity for discussion, participation, and critique. The course will meet Tuesdays and Thursdays from 10:15 to 11:45, with the first meeting on Tuesday August 30.

The course will involve advanced mathematical material and will cover formal proofs in detail, and will be taught at the doctoral level. While there are no specific formal prerequisites, background or courses in algorithms, complexity theory, discrete math, combinatorics, convex optimization, probability theory and statistics will prove helpful, as will "mathematical maturity" in general. We will be examining detailed proofs throughout the course. If you have questions about the desired background, please ask. Auditors and occasional participants are welcome.

The course requirements for registered students will be a mixture of active in-class participation, problem sets, possibly leading a class discussion, and a final project. The final projects can range from actual research work, to a literature survey, to solving some additional problems.

MEETING/TOPIC SCHEDULE

The exact timing and set of topics below will depend on our progress and will be updated as we proceed.

Module 1
Course overview, topics, and mechanics. Analysis of rectangle learning problem. Introduction of the PAC learning model. PAC learning conjunctions. Intractability of PAC learning 3-term DNF. PAC learning 3-term DNF by 3CNF.

Course Overview Lecture Notes

Rectangle Learning Problem Lecture Notes

PAC Model Lecture Notes

K&V Chapter 1

Module 2
Consistency and PAC learning in the finite H case. Consistency and compression.

Consistency and Compression Lecture Notes

K&V Chapter 2.

Module 3
Consistency and PAC learning in the infinite H case. The VC dimension. Uniform convergence.

VC Dimension Lecture Notes