Hands-On Learning Theory

Semester:	2024 Semester 2
Time and place:	The University of Melbourne, Monday an Wednesday, 4.30-6.00pm, Melbourne Connect 3203
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
Mon, Jul 29	Lecture 3: Fano's inequality, empirical risk minimization with a finite hypothesis class
Wed, Jul 31	(lecture continues)
Mon, Aug 5	Lecture 1: Markov's inequality, Chebyshev's inequality
Wed, Aug 7	Lecture 2: Hoeffding's inequality, empirical risk minimization with a finite hypothesis class
Mon, Aug 12	Lecture 5: McDiarmid's inequality, sub-Gaussian random variables	Homework 0 solution Homework 1: due on Aug 16, 11.59pm AEDT
Wed, Aug 14	Submodular optimization Greedy algorithms for submodular maximization
Mon, Aug 19	Lecture 7: deterministic and stochastic optimization, convergence rates	Homework 1 solution
Wed, Aug 21	(lecture continues)	Homework 2: due on Aug 29, 11.59pm AEDT
Mon, Aug 26	Lecture 9: primal-dual witness method, support recovery
Wed, Aug 28	(lecture continues)	Homework 2 solution