CS 4301: Numerical Methods for Machine Learning and Data Science

Fall 2020

An introduction to computational methods in linear algebra and numerical optimization methods with the aim of preparing students for higher level electives in data science, artificial intelligence, and machine learning. Learning outcomes:

• Ability to apply gradient descent to find local optima of differentiable functions
• Practical and theoretical understanding convex functions and convex sets
• Ability to solve constrained optimization problems via the method of Lagrange multipliers
• Ability to understand the precision issues that arise when applying iterative numerical methods to solve optimization problems
• Ability to formulate basic results in linear algebra as convex optimization problems (regression, projections, eigenvalues)
• Understand the differences, both practical and theoretical, between different matrix decomposition techniques

Where: Online
When: MW, 10:00am-11:15am

Instructor: Nicholas Ruozzi
Office Hours: M 11:30-12:30, W 12:30pm-1:30pm, and by appointment online.

TA: Shahab Shams
Office Hours: R 10:30am - 12:30pm

Grading: problem sets (70%), midterm (15%), final (15%)

Required Prerequisites: CS3345, Data Structures and Algorithms
Recommended Prerequisites: MATH 2413 (Differential Calculus) or MATH 2417 (Calculus I) and MATH 2418 (Linear Algebra). Comfort with programming, basic probability, and algorithms is also assumed.

Week	Dates	Topic	Readings
1	Aug. 17 & 19	Introduction Gradients and Multivariable Calculus
2	Aug. 24 & 26	Convex Sets and Convex Functions Gradient Descent	Boyd 2.1-2.3 Boyd 9.1-9.3 (can skip example subsections)
3	Aug. 31 & Sept. 2	Subgradient Methods Convex Optimization	Boyd 9.1-9.3 Boyd 4.1-4.3
4	Sept. 9	Projected Gradient
5	Sept. 14 & 16	Duality and Lagrange Multipliers	Boyd 5
6	Sept. 21 & 23	Constraint Qualification and KKT	Boyd 5
7	Sept. 28 & 30	Second Order Methods	Boyd 3.3, 9.5, 10.1-10.2
8	Oct. 5 & 7	ML Applications
9	Oct. 12 & 14	Linear Algebra Review Positive Semidefinite Matrices	Boyd A.5
10	Oct. 19 & 21	Eigenvectors, Eigenvalues, and Semidefinite Programming	Boyd A.5
11	Oct. 26 & 28	Singular Value Decomposition
12	Nov. 2 & 4	Midterm Discussion & More SVD
13	Nov. 9 & 11	Matrix Factorizations	CUR Decompositions
14	Nov. 16 & 18	Submodular Functions Alternating Projections
15	Nov. 23 & 25	Proximal Gradient Review

All problem sets will be available on eLearning and are to be turned in there. See the homework guidelines below for homework policies.

There is no required textbook, but the following books may serve as useful references for different parts of the course.

• Convex Optimization by Stephen Boyd and Lieven Vandenberghe (online) .
• Convex Optimization Theory by Dimitri P. Bertsekas

All exams will be take home, open book, open notes.
Midterm: 10/14, Take Home
Final: TBD, during exam period

I expect you to try solving each problem set on your own. However, if you get stuck on a problem, I encourage you to collaborate with other students in the class, subject to the following rules:

1. You may discuss a problem with any student in this class, and work together on solving it. This can involve brainstorming and verbally discussing the problem, going together through possible solutions, but should not involve one student telling another a complete solution.
2. Once you solve the homework, you must write up your solutions on your own, without looking at other people's write-ups or giving your write-up to others.
3. In your solution for each problem, you must write down the names of any person with whom you discussed it. This will not affect your grade.
4. Do not consult solution manuals or other people's solutions from similar courses - ask the course staff, we are here to help!

Late homework will NOT be accepted except in extreme circumstances or those permitted by university policy (e.g., a religious holiday). All such exceptions MUST be cleared in advance of the due date.

UT Dallas Course Policies and Procedures

For a complete list of UTD policies and procedures, see here.