CS 59000-MLT: Machine Learning Theory Seminar

Semester: Fall 2015, also offered on Fall 2016
Time and place: Tuesday and Thursday, 12pm-1.15pm, Pao Hall of Visual & Performing Arts B157
Instructor: Jean Honorio
Office hours: Tuesday and Thursday, 3.30pm-4.30pm, Lawson Building 2142-J
For appointments outside office hours, please send me an e-mail.

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 this seminar, 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, this seminar 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 seminar 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.

Learning Objectives

Upon completing the course, students should be able to use different techniques for:

Prerequisites

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 course.

Assignments

There will be four homeworks, one paper review and one project (dates posted on the schedule). The homeworks and the project are to be done individually. The paper review is to be done either individually or in groups of two students.

The homeworks will be on problems for which the answer is known. The project will be on a problem for which the answer is not known or only partially known.

For the paper review and the project, please pick a relevant topic according to your study goals. I encourage you to pick a paper and project on the same/similar topic. In case you do not have a topic, I can potentially assign you one. I encourage you to pick your topic as soon as possible.

For the paper review, you will write a 2-4 page review of a paper (around 1-2 weeks before the midterms). The goal is to learn to read technically demanding papers critically, and hopefully in the process, generate novel research ideas. Your review should not only summarize the main result of the paper, but critique it, instantiate it on examples, discuss its overall significance, and suggest possible future directions.

For the project, you will write a half-page project plan (in the beginning of the semester), a 2-4 page preliminary results report (around 1-2 weeks after the midterms) and a 4-8 page final results report (around the final exam date). The goal of the project is to apply some of the techniques learnt in class to a particular machine learning problem. Remember, the goal of the course is to learn how to prove theorems regarding sample complexity. Proposing a small modification to a current algorithm that allows proving aspects of the algorithm's behavior is also welcome. For an example click here (password-protected).

Grading

Homeworks: 30%
Paper review: 20%
Project (preliminary results): 20%
Project (final results): 30%

Late policy

Assignments are to be submitted by the due date listed. Each person will be allowed seven days of extensions which can be applied to any combination of assignments during the semester. Use of a partial day will be counted as a full day. Extensions cannot be used after the final day of classes. Please, use the extension days wisely!

Assignments will NOT BE accepted if they are more than five days late.

Academic Honesty

Please read the departmental academic integrity policy here. This will be followed unless we provide written documentation of exceptions. We encourage you to interact amongst yourselves: you may discuss and obtain help with basic concepts covered in lectures and homework specification (but not solution). However, unless otherwise noted, work turned in should reflect your own efforts and knowledge. Sharing or copying solutions is unacceptable and could result in failure. You are expected to take reasonable precautions to prevent others from using your work.

Additional course policies

Please read the general course policies here.

Schedule

Date Topic (Tentative) Notes
Tue, Aug 25 Introduction and Lecture 1: Markov's inequality, Chebyshev's inequality
Thu, Aug 27 Lecture 2: Hoeffding's inequality, empirical risk minimization with a finite hypothesis class
Tue, Sep 1 Lecture 3: Fano's inequality, empirical risk minimization with a finite hypothesis class Homework 1 (password-protected): due on Sep 3 at beginning of class
Thu, Sep 3     (lecture continues) Homework 1 due
Tue, Sep 8 Lecture 4: probably approximately correct (PAC) Bayes, structured prediction Homework 1 solution (password-protected)
Thu, Sep 10     (lecture continues) Send me an e-mail with a link to the paper you plan to review
Tue, Sep 15 Lecture 5: McDiarmid's inequality, sub-Gaussian random variables Project plan due (moved to Sep 22)
Thu, Sep 17     (lecture continues) Homework 2 (password-protected): due on Sep 24 at beginning of class
Tue, Sep 22 Lecture 6: Rademacher complexity, linear prediction Project plan due (see Assignments for details)
Thu, Sep 24     (lecture continues) Homework 2 due
Tue, Sep 29 Lecture 7: deterministic and stochastic optimization, convergence rates Homework 2 solution (password-protected)
Thu, Oct 1     (lecture continues) Paper review due (moved to Oct 6)
Tue, Oct 6 Paper review due (see Assignments for details)
Thu, Oct 8
Tue, Oct 13 OCTOBER BREAK
Thu, Oct 15 Lecture 8: restricted strong convexity, compressed sensing
Tue, Oct 20     (lecture continues)
Thu, Oct 22 Lecture 9: primal-dual witness method, support recovery Preliminary project report due (moved to Oct 27)
Tue, Oct 27     (lecture continues) Preliminary project report due (see Assignments for details)
Thu, Oct 29     (lecture continues) Homework 3 (password-protected): due on Nov 5 at beginning of class
Tue, Nov 3 Project presentations (25-30 min per person)
Thu, Nov 5     (presentations continue) Homework 3 due
Homework 4 (password-protected): due on Nov 12 at beginning of class
Tue, Nov 10     (presentations continue) Homework 3 solution (password-protected)
Thu, Nov 12     (presentations continue) Homework 4 due
Tue, Nov 17 Lecture 10: growth function, Vapnik-Chervonenkis (VC) dimension, Sauer-Shelah lemma, Massart lemma Homework 4 solution (password-protected)
Thu, Nov 19     (lecture continues)
Tue, Nov 24     (lecture continues)
Thu, Nov 26 THANKSGIVING VACATION
Tue, Dec 1 Lecture 11: scaled uniform convergence Final project report due (see Assignments for details)
Thu, Dec 3
Tue, Dec 8
Thu, Dec 10     (lecture continues)