Hands-On Learning Theory

Semester: 2024 Semester 1
Time and place: The University of Melbourne, Wednesday and Friday, 11am-12.30pm, Melbourne Connect 3201
Organizer: Jean Honorio

Imagine you run your favorite machine learning algorithm and obtain impressive results. Some weeks later, you collect more data and your algorithm does not perform very well. What happened? Is your algorithm wrong? Do you need to collect more data for learning? Should you use another algorithm?

In these meetings, we will analyze when an algorithm works or not, with respect to several aspects, such as how much training data is needed, how much computation, etc. We will learn the main tools for proving theorems and proposing new algorithms, proving their convergence, necessary/sufficient number of samples, etc.

Technically speaking, these meetings will mainly focus on non-asymptotic analysis of the convergence and statistical efficiency of algorithms. We will introduce several concepts and proof techniques from statistical learning theory, information theory and optimization. The meetings will include topics such as concentration bounds, empirical risk minimization, PAC-Bayes, Rademacher/Gaussian complexity, Karush-Kuhn-Tucker conditions, primal-dual witness, convergence rates, restricted strong convexity, Fano's inequality, etc.

Basic knowledge from calculus and linear algebra is required. Some knowledge or experience with machine learning or data mining is welcome. Necessary concepts from statistics and optimization will be provided during the meetings.

Schedule

Date Topic (Tentative) Notes
Wed, Jan 28 Lecture 1: Markov's inequality, Chebyshev's inequality
Fri, Mar 1 Lecture 2: Hoeffding's inequality, empirical risk minimization with a finite hypothesis class
Wed, Mar 6 Lecture 3: Fano's inequality, empirical risk minimization with a finite hypothesis class Homework 0 solution
Homework 1: due on Mar 13, 11.59pm AEDT
Fri, Mar 8     (lecture continues)
Wed, Mar 13 Lecture 5: McDiarmid's inequality, sub-Gaussian random variables Homework 1 solution
Fri, Mar 15 Lecture 9: primal-dual witness method, support recovery Homework 2: due on Mar 22, 11.59pm AEDT
Wed, Mar 20     (lecture continues)
Fri, Mar 22 Lecture 11: Le Cam's lemma Homework 2 solution
Wed, Mar 27 Lecture 8: restricted strong convexity, compressed sensing
Fri, Mar 29     (lecture continues)