Machine Learning Theory (CSCI599)
This introductory graduate course will focus on developing the core concepts and techniques of machine learning theory. We will examine the inherent abilities and limitations of learning algorithms in well-defined learning models. Specifically, the course will focus on algorithmic problems in supervised learning. The goal of supervised learning is to infer a function from a set of labeled observations. We will study algorithms for learning Boolean functions from labeled examples in a number of models (online learning, PAC learning, SQ learning, learning with noise, etc.).
The course is primarily targeted toward graduate students who want to gain familiarity with algorithmic and statistical tools for machine learning. Advanced undergraduate students with sufficient mathematical maturity are welcome.
- Instructor: Ilias Diakonikolas
Office Hours: By appointment (send me an email).
- Teaching Assistant: Ehsan Emamjomeh-Zadeh
Office Hours: Mondays, 3:15 - 4:30, SAL 246 (location subject to change).
- Lectures: Tuesdays 15:30-18:50, WPH 106.
Mathematical maturity. Solid background in algorithms, linear algebra, and probability.
Here is an outline of the course material:
- Online Learning: Winnow, Best Experts, Weighted Majority
- PAC Learning, Relation to Online Learning, Occam's Razor
- VC Dimension and Sample Complexity
- Learning Decision Trees and DNFs
- Learning with Noise: Classification Noise, Malicious Noise
- Statistical Query Learning
- Distribution Dependent Learning, Fourier Transform
- Computational Hardness of Learning
- Learning with Membership and Equivalence Queries
- Other Models of Learning: Semi-supervised Learning, Active Learning
- Lecture 1 (January 10) Introduction to machine learning theory.
Supervised Learning. Introduction to Online Learning.
- Lecture 2 (January 17) Online Learning: Winnow algorithm, Perceptron algorithm.
- Lecture 3 (January 24) Generic Bounds for Online Learning (halving algorithm, weighted majority), VC dimension. Introduction to PAC learning.
- Lecture 4 (January 31) PAC Learning model, online to PAC conversion, Occam's razor, application to learning sparse disjunctions.
- Lecture 5 (February 7) Chernoff Bounds, proper versus improper learning, learning 3-term DNFs.
- Lecture 6 (February 21) VC dimension, sample complexity of PAC learning.
- Lecture 7 (February 28) Weak and Strong Learning. Introduction to Boosting: Schapire's boosting, Adaboost.
- Lecture 8 (March 7) PAC Learning with Noise: Random Classification Noise, Malicious Noise.
- Lecture 9 (March 21) Statistical Query (SQ) Learning: Simulating SQ Queries in the presence of Random Classification Noise.
- Lecture 10 (March 28) Cryptographic Hardness of Learning.
- Lecture 11 (April 4) Learning via PTF degree. Introduction to Fourier Analysis.
- Lecture 12 (April 11) Fourier Analysis continued. PAC Learning under the Uniform Distribution: Low-Degree Algorithm
Homework Assignments: There will be 4/5 homework assignments that will count for 60% of the grade. The assignments which will be proof-based, and are intended to be challenging.
Collaboration and discussion among students is allowed, though students must write up their solutions independently.
- First Homework: [pdf] (due on February 7)
- Second Homework: [pdf] (due on February 28)
Course Project: A part of the course (25% of the grade) is an independent project on a topic related to machine learning theory. Projects can be completed individually or in groups of two students.
- Third Homework: [pdf] (due on April 4)
The goal of the project is to become an expert in an area related to the class material, and potentially contribute to the state of the art. There are two aspects to the course project. The first is a literature review: Students must decide on a topic and a list of papers, understand these papers in depth, and write a survey presentation of the results in their own words. The second aspect is to identify a research problem/direction on the chosen topic, think about it, and describe the progress they make.
Students must consult with the instructor during the first half of the course for help in forming project teams, selecting a suitable project topic, and selecting a suitable set of research papers.
Students will be graded on the project proposal (5%), the progress report (5%), and the final report (15%).
The remaining part of the grade will be based on class participation (15%).
The textbook for this course is:
An additional textbook (available online) we will use is:
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