Course Description
The course will cover fundamental mathematical and computational methods needed to implement computational imaging and machine learning solutions. First, relevant aspects of probability theory, matrix decompositions, and vector calculus will be introduced. Subsequently, methods that underline approximate inference, such as stochastic sampling methods, are introduced. Finally, numerical optimization methods that represent core components of computed imaging and machine learning will be introduced. This will include numerical optimization-based formulations of inverse problems. An emphasis will be placed on first-order deterministic and stochastic gradient-based methods. Second-order optimization techniques including quasi-Newton and Hessian-free methods will also be surveyed. The application of these methods to computed imaging and machine learning problems will be addressed in detail.
Learning Objectives
Upon completion of this course, the students will be able to
Demonstrate the ability to formulate the solution of computed imaging and machine learning problems as numerical optimization problems
To enable students to apply cutting edge optimization techniques to solve computed imaging and machine learning problems
To enable students to understand the pros and cons of various numerical optimization techniques and to customize solutions for new problems that arise in practice
Understand the difference and relative advantages of deterministic vs stochastic optimization methods
Understand the basic principles of variational Bayesian inference and how it relates to a numerical optimization problem
Understand the basic principles of how to sample from a high-dimensional probability distribution
Grading
Homework: 30% (3 HWs, each 10%)
Machine Problems: 40% (4 MPs, each 10%)
Project: 30% (Final project presentation: 10%; Final project report and code: 20%)
(No exams)
Resources
Mathematics for Machine Learning, M. Deisenroth, A. Faisal, and C. Ong, Cambridge University Press (free online version)
Additional reading material will be assigned from a combination of book chapters, review articles, and primary research papers
Office hours & contact
Prof. Yogatheesan Varatharajah:
Tuesday - 3:30pm to 4:30pm (after class)
Location - Everitt Lab 3213
Contact - varatha[number2][at]illinois[dot]edu
Please include "[BIOE 485]" in email title!
(TA) Nimit Kapadia:
Wednesday - 3:30pm to 4:30pm
Location - Everitt Lab 3213
Contact - nimithk[number2][at]illinois[dot]edu
Please include "[BIOE 485]" in email title!