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Technical University of Munich

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Convex Optimization for Machine Learning and Computer Vision (IN2330) (2h + 2h, 6 ECTS)

Announcement:
- The post-exam review (Klausureinsicht) for the repeat exam will take place on Thursday, November 2nd from 11:00 - 12:00 in the room 02.07.011B.
- The post-exam review (Klausureinsicht) will take place on Wednesday, August 23th from 16:00 - 18:00 in the room 02.09.023.

Many important machine learning, computer vision and image processing problems can be cast as convex energy minimization problems, e.g. training of SVMs, logistic regression, low-rank and sparse matrix decomposition, denoising, segmentation, or multiframe blind deconvolution. In this lecture we will discuss first order convex optimization methods to implement and 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 or the alternating directions methods of multipliers. This lecture will cover the mathematical background needed to understand why the investigated methods converge as well as the efficient practical implementation.

We will cover the following topics:

Elements in convex analysis

  • Convex set and convex function
  • Existence and uniqueness of minimizers
  • Subdifferential
  • Convex conjugate
  • Duality

Numerical methods

  • Gradient-based methods, Majorization-minimization algorithm, line search method
  • Proximal algorithms, primal-dual hybrid gradient method, alternating direction method of multipliers
  • Convergence analysis
  • Acceleration techniques

Bilevel optimization

  • Generalized implicit function theorem
  • Adjoint approach for numerical solution

Example applications in machine learning and computer vision include

  • Low-rank and sparse matrix decomposition
  • Training of SVMs, Logistic regression
  • Total-variation image restoration
  • Image segmentation
  • Parameter learning
  • Implementation in MATLAB and Python

Lecture

Location: 02.09.023
Time and Date: Wednesday 16:15 - 18:00
Lecturer: Dr. Tao Wu
Start: April 26th, 2017
The lecture is held in English.

Exercises

Location: 02.09.023
Time and Date: Monday 12:15 - 14:00
Organization: Thomas Möllenhoff, Emanuel Laude
Start: May 8th, 2017
The exercise sheets consist of two parts, theoretical and programming exercises. The upcoming exercise sheets will be made available before the lecture each Wednesday, and you have one week to solve it. Please hand in your solution to the theory exercises after the lecture on Wednesday. The solutions will be discussed in the Monday exercise class the week after. Please submit the programming solutions as a zip file with filename "matriculationnumber_firstname_lastname.zip" ONLY(!) containing your .m-files (no material files) via email to cvx4cv-ss17@vision.in.tum.de until Wednesday 23:59. Please remember to write CLEAN(!), COMMENTED(!) code! You are allowed to work on the exercise sheets in groups of two students.

The exercise sheets can be accessed here.

Bonus

By achieving at least 60% of all possible points on the exercise sheets you can obtain a bonus of 0.3 in the final exam. Note that you can neither improve a 1.0 nor a 5.0.

Exam

Location: Room 5620.01.101 (101, Interims Hörsaal 1)
Time and Date: Wednesday, 9th of August, 2017, 13.30h-15.30h.

You may only use standard writing materials and one handwritten double-sided A4 sheet of notes. You are not allowed to use any electronic devices.

Lecture Material

Course material (slides and exercise sheets) can be accessed here.

Send us an email if you need the password.

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Informatik IX
Chair of Computer Vision & Artificial Intelligence

Boltzmannstrasse 3
85748 Garching info@vision.in.tum.de

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