**PENN CIS 625, SPRING 2015: COMPUTATIONAL LEARNING THEORY
**

Prof. Michael Kearns

mkearns@cis.upenn.edu

Dr. Grigory Yaroslavtsev

grigory.yaroslavtsev@gmail.com

Time: Mondays
12-3 PM

Location: 303 Towne and 307 Levine
(we'll use both locations depending on the week, in order to be able to serve lunch)

**IMPORTANT NOTE:**
The first course meeting will be on
**Monday Jan 26.**

URL for this page:

www.cis.upenn.edu/~mkearns/teaching/COLT

Previous incarnations of this course:

www.cis.upenn.edu/~mkearns/teaching/COLT/colt12.html (with Jake Abernethy)

www.cis.upenn.edu/~mkearns/teaching/COLT/colt08.html (with Koby Crammer)

**COURSE DESCRIPTION**

This course is an introduction to Computational Learning Theory, a field which attempts to provide algorithmic, complexity-theoretic and probabilistic foundations to modern machine learning and related topics.

The first part of the course will closely 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. Copies of K&V will be available at the Penn bookstore. 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 problems and techniques typically studied in Computational Learning Theory, and provide a basic arsenal of powerful mathematical tools for analyzing machine learning problems.

Topics likely to be covered include:

Additional topics we may also cover include:

**COURSE FORMAT, REQUIREMENTS, AND PREREQUISITES **

Much of the course will be in fairly traditional "chalk talk" lecture format, but with ample opportunity for discussion, participation, and critique. The course will meet once a week on Mondays from 12 to 3 (but see note above about the first meeting). Lunch will be served.

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, 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 some to-be-determined 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.

Mon Feb 2

[MK; meeting in Levine 307]

Mon Feb 9

[MK; meeting in Levine 307]

Mon Feb 16

[MK; meeting in Towne 303]

Sample complexity bounds via the Vapnik-Chervonenkis dimension, continued.

Mon Feb 23

[MK; meeting in Levine 307]

VC dimension wrap-up. Learning with classification noise.

Mon Mar 2

[MK; meeting in Levine 307]

Classification noise and the statistical query model.

Mon Mar 9

Spring break, no meeting

Mon Mar 16

[MK; meeting in Levine 307]

Mon Mar 23

[MK; meeting in Towne 303]

Mon Apr 6

[GY; meeting in Towne 303]

Much of this material is covered in Ryan O'Donnell's book "Analysis of Boolean Functions", which can be downloaded here.

Here are slides for these lectures.

Mon Apr 13

[GY; meeting in Levine 307]

More Fourier Fun. Here are slides for these lectures.

Mon Apr 20

[GY; meeting in Levine 307]

Learning and Testing Submodular Functions. Here are slides for these lectures.

Mon Apr 27

[GY; meeting in Levine 307]

L_p testing. Here are slides for these lectures.

INFORMATION ON COURSE PROJECTS.

For those of you registered for credit in the course, your final assignment will be a course project, for which you have three choices:

For your final projects, you should work alone. You are welcome to send email to Prof Kearns proposing what your final project will be in order to get feedback and advice.

The deadline for final projects will be May 10, via email to Prof Kearns.