**PENN CIS 625, FALL 2020: THEORY OF MACHINE LEARNING
**

Prof. Michael Kearns

mkearns@cis.upenn.edu

Time:
Tuesdays and Thursdays 10:30AM-Noon

Location:
Virtual lectures via Zoom at
this URL.
All students are strongly encouraged to attend lectures "live" and with video on to
increase engagement and interaction. However, all lectures will be recorded and notes
provided to accomodate those in other time zones.

Office Hours:
Prof. Kearns will hold office hours from noon to 1PM after each Tuesday's lecture at
this URL.

URL for this page:

www.cis.upenn.edu/~mkearns/teaching/COLT/CIS625

Previous incarnations of this course:

www.cis.upenn.edu/~mkearns/teaching/COLT/colt18.html

www.cis.upenn.edu/~mkearns/teaching/COLT/colt17.html

www.cis.upenn.edu/~mkearns/teaching/COLT/colt16.html

www.cis.upenn.edu/~mkearns/teaching/COLT/colt15.html (with Grigory Yaroslavtsev)

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 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. Copies of K&V will be available at the Penn bookstore; I'm also looking into providing electronic access, as I do for the first chapter in the schedule below. 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:

**COURSE FORMAT, REQUIREMENTS, AND PREREQUISITES **

Much of the course will be in fairly traditional "chalk talk" lecture format (virtually on Zoom), but with ample opportunity for discussion, participation, and critique. The course will meet Tuesdays and Thursdays from 10:30 to noon, with the first meeting on Tuesday September 1.

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.

Thu Sep 3

Model, algorithm and analysis for the rectangle learning problem.

Tue Sep 8

Introduction to the PAC model.

Thu Sep 10

Learning Boolean conjunctions in the PAC learning model.

Tue Sep 15

Hardness of PAC-learning 3-term DNF.

Thu Sep 17

PAC learning 3-term DNF learnability by 3CNF. Introduction to consistency, compression and learning.

Tue Sep 22

Consistency, compression and learning, continued.

Thu Sep 24

Consistency, compression and learning, continued. Discussion of Problem Set 1.

Tue Sep 29

Introduction to the VC dimension.

Thu Oct 1

VC dimension continued: Sauer's Lemma.

Tue Oct 6

VC dimension continued: probalistic analysis, two-sample trick.

Thu Oct 8

VC dimension continued: sample size lower bounds; structural risk minimization; distribution-dependent improvements.

Tue Oct 13

VC dimension finished (finally): data-dependent improvements; other loss functions. Musings on Problem Set 1.

Thu Oct 22

More musings on Problem Set 1; introduction to learning with classification noise (CN).

Tue Oct 27

Learning with CN continued; the statistical query (SQ) model.

Thu Oct 29

The SQ model continued: SQ learning implies CN learning; hardness of parity functions in SQ.

Tue Nov 3

The SQ model continued: the SQ dimension; hardness of learning decision trees and DNF in the SQ model.

Thu Nov 5

The PAC Solar System: containments and separations; cryptographic hardness; PAC with membership queries. Preview of Problem Set 2.

Tue Nov 10

Boosting: model and problem formulation; Schapire's ternary majority construction.

Thu Nov 12

Adaboost: algorithm and analysis; connection to weak and strong PAC learning.

Tue Nov 17

Introduction to no-regret learning; Multiplicative Weights algorithm and analysis.

Thu Nov 19

MW analysis continued; discussion and connection to PAC; lower bounds on regret.

Tue Nov 24

No-regret learning and game theory; the minimax theorem.

Tue Dec 1

Fairness in ML: introduction; group fairness definitions; where ML can go wrong.

Thu Dec 3

Fairness continued: a post-processing approach and algorithm; error-unfairness Pareto frontiers.

Tue Dec 8

Fairness continued: endogenizing fairness into training; game-theoretic/no-regret approach; individual/metric fairness; fine-grained subgroup fairness.