PENN CIS 625, SPRING 2016: COMPUTATIONAL LEARNING THEORY (original) (raw)

IMPORTANT NOTE:The first course meeting will be onWeds Jan 13 from 12-3, and held in Greenberg Lounge of Skirkanich Hall.

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 ofAn 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.

PAC-style Analyses in Probabilistic Inference

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.

DETAILED MEETING/TOPIC SCHEDULE The exact timing and set of topics below will depend on our progress and will be updated as we proceed.

Wed Jan 13
In the first meeting, we will go over course mechanics and present a course overview, then immediately begin investigating the Probably Approximately Correct (PAC) model of learning. Detailed topics covered: Learning rectangles in the real plane; definition of the PAC model; PAC-learnability of rectangles in d dimensions.

READING: K&V Chapter 1.

Mon Jan 18
No lecture, MLK holiday.

Mon Jan 25
No lecture, Prof Kearns out of town.

Mon Feb 1
PAC-learnability of conjunctions of boolean variables. Intractability of PAC-learning 3-term DNF; learning 3-term DNF by 3CNF and the importance of hypothesis representation.

Mon Feb 8
Sample complexity and the Vapnik-Chervonenkis dimension.

Mon Feb 15
Guest lecture by Jamie Morgenstern; sample complexity of auctions.

Mon Feb 22
Representation-independent intractable ("truly hard") learning problems via cryptography.

Mon Feb 29
Learning and cryptography continued; introduction to boosting.

Mon Mar 7
Spring Break, no lecture.

Mon Mar 14
Boosting continued: Adaboost and top-down decision tree learning.

Problem Set --- Due in hardcopy format in class, Monday April 11:K&V: 1.1, 1.3, 3.1, 3.2, 4.3, 5.2, 5.6, 8.1, 8.3. You are free to collaborate on the problem set, but please turn in separate write-ups and acknowledge your collaborations. Please do not attempt to look up solutions in the literature.

Mon Mar 21
Learning with noise and the statistical query model.

Mon Mar 28
Guest lecture by Steven Wu; statistical query learning and differential privacy.

Mon Apr 4
Learning with membership and equivalence queries: deterministic finite automata.

Mon Apr 11
TBD.

Mon Apr 17
TBD.