Convex Optimization for Machine Learning and Computer Vision (IN2330) (2h + 2h, 6 ECTS)
Many important machine learning and computer vision tasks can be formulated as convex optimization problems, e.g. training of SVMs, logistic regression, low-rank and sparse matrix decomposition, image segmentation, stereo matching, surface reconstruction, etc. In this lecture we will discuss first-order convex optimization methods to solve the aforementioned problems efficiently. Particular attention will be paid to problems including constraints and non-differentiable terms, giving rise to methods that exploit the concept of duality such as the primal-dual hybrid gradient method and the alternating directions methods of multipliers. This lecture will cover the mathematical background needed to understand why these methods converge as well as the details of their efficient implementation.
We will cover the following topics:
Elements in convex analysis
- Convex sets and convex functions
- Existence and uniqueness of minimizers
- Convex conjugates
- Saddle point problems and duality
- Gradient-based methods
- Proximal algorithms, primal-dual hybrid gradient method, alternating direction method of multipliers
- Convergence analysis
- Acceleration techniques, stopping criteria
Examplary applications in machine learning and computer vision include
- Training of SVMs, Logistic regression
- Image reconstruction (e.g. denoising, deblurring, inpainting)
- Low-rank and sparse matrix decomposition
We will implement some of them in MATLAB.
Location: Room 01.09.014
Time and Date: Monday 16:15 - 18:00
Start: October 22nd, 2018
Lecturer: Dr. Tao Wu
The lecture is held in English.
The exercise sheets consist of two parts, theoretical and programming exercises.
Exercise sheets will be posted every Monday and are due a week later. You will have one week to do the exercises.
Please submit the programming solutions as a zip file with filename “matriculationnumber_firstname_lastname.zip” only! containing your code-files (no material files) via email to firstname.lastname@example.org, and hand in the solutions to the theoretical part in Monday's lecture. We will give you back the corrected sheets on Wednesday when we discuss them in class.
Please remember to write clean, commented(!) code! You are allowed to work on the exercise sheets in groups of two students.
The first exercise sheet that counts to the exam bonus is exercise sheet 1, which is due Monday, 29th of October.
The exercise sheets can be accessed here.
To achieve the bonus, you have to meet two requirements:
1. get at least 75% grades of all exercises totally, i.e. sum of the grades you get in all exercises divided by the grades of all exercises (without bonus) should be >= 0.75
2. present your theoretical solution during tutorial at least once in this semester.
You cannot improve either 1.0 or >4.0.
Course material (slides and exercise sheets) can be accessed here.
Send us an email if you need the password.