EECS 496 - Computational Learning Theory
Northwestern University
Winter 2019


This course will introduce some of the central topics in computational learning theory, a field which approaches the question "whether machines can learn" from the perspective of theoretical computer science. We will study well defined and rigorous mathematical models of learning where it will be possible to give precise and rigorous analysis of learning problems and algorithms. A big focus of the course will be the computational efficiency of learning in these models. We will develop some provably efficient algorithms and explain why such provable algorithms are unlikely for other models.

We will only cover topics which permit a mathematically rigorous analysis and hence mathematical maturity is absolutely necessary. In particular, some familiarity with basic probability (such as linearity of expectation) and basic linear algebra will be necessary. Also, the emphasis of the course will be on proofs, so if you are in this course, you should enjoy proofs and math.

Example topics include inductive inference, query learning, PAC learning and VC theory, Occam's razor, online learning, boosting, support vector machines, bandit algorithms, statistical queries, Rademiacher complexity, and neural networks.

Basic Information

Instructor: Lev Reyzin
Syllabus: pdf
Time and Location: Tu,Th 9:30-10:50am, Tech MG28
Required Textbook: Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar. Foundations of Machine Learning, 2nd edition
Optional Textbook: Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning: From Theory to Algorithms
Office Hours: Tu 11:00-11:50am, F 10:00-10:50am

Exam Dates

Final exam: Tuesday, 03/19/2019 at 12:00-2:00pm

Problem Sets

problem set 1 due 2/12/19

Lectures and Readings

Note: lectures will have material not covered in the readings.

Lecture 1 (1/8/19)
covered material: intro to the course, preview of learning models, inductive inference from text and informant
reading: Language Idenification in the Limit by Gold (1967)
optional reading: section 7 of Computing Machinery and Intelligence by Turing (1950)

Lecture 2 (1/10/19)
covered material: efficient exact learning with MQs and EQs, L* algorithm learning regular languages, implication for learning in limit
reading: ch. 16.1, 16.2, 16.3.3, 16.4 up to (but not including) 16.4.1
optional reading: ch. 16.4.1

Lecture 3 (1/15/19)
covered material: intro to PAC learning, relating PAC + MQ to query learning
reading: intro to ch. 2, 16.3.2

Lecture 4 (1/17/19)
covered meterial: PAC learning of axis-aligned regtangles; PAC guarantees for finite realizable case
reading: ch. 2.1, 2.2 A Theory of the Learnable by Valiant (1984)
optional reading: Occam's Razor by Blumer et al. (1986)

Lecture 5 (1/22/18)
covered material: learning in non-realizable case, introduction to Rademacher complexity, useful inequalities
reading: ch. 2.3, 3.1
optional reading: ch. 2.4

Lecture 6 (1/24/19)
covered material: Rademacher generalization bounds, growth function, VC dimension
reading ch. 3.2
optional reading: Rademacher Penalties and Structural Risk Minization by Koltchinskii (2001)

Lecture 7 (1/29/19)
covered material: VC generalization bounds
reading: ch. 3.3
other: problem set 1 assigned

Lecture 8 (2/5/19)
covered material: weak learning, boosting and equivalence to strong learning
reading: ch. 7.1 and 7.2
other: slides from lecture

Lecture 9 (2/7/19)
covered material: margins and the margin bound for boosting
reading: ch. 7.4 and 7.6
other: continued slides from lecture
optional reading: How Boosting the Margin Can Also Boost Classifier Complexity by Reyzin and Schapire (2006)

Lecture 10 (2/12/19)
covered material:the statistical query (SQ) model, relationship to PAC and noicy PAC, SQ variants SQ dimension
reading: Efficient Noise-Tolerant Learning from Statistical Queries by Kearns (1998)
other: slides from lecture