Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Optimization for Data Science (2020)

Lecturers: Bernd Gärtner (CAB G31.1);
David Steurer (CAB H37.1).
Assistants: Tommaso D'Orsi (CAB H37.2);
Hung Hoang (CAB G19.2), contact assistant;
Saeed Ilchi (CAB G32.1);
Gleb Novikov (CAB H36.2);
Yiming Yan.
Lectures: Mon 15-16, ETF C1,
Tue 10-12, ETF C1.
Credit Points: 8CP (261-5110-00L, 3V + 2U + 2A)
Language: English
Contents: This course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science.
  • In the first part of the course, we will discuss how classic first and second order methods such as gradient descent and Newton's method can be adapted to scale to large datasets, in theory and in practice. We also cover some new algorithms and paradigms that have been developed specifically in the context of data science. The emphasis is not so much on the application of these methods (many of which are covered in other courses), but on understanding and analyzing the methods themselves.
  • In the second part, we discuss convex programming relaxations as a powerful and versatile paradigm for designing efficient algorithms to solve computational problems arising in data science. We will learn about this paradigm and develop a unified perspective on it through the lens of the sum-of-squares semidefinite programming hierarchy. As applications, we are discussing non-negative matrix factorization, compressed sensing and sparse linear regression, matrix completion and phase retrieval, as well as robust estimation.
Moodle: All materials in the course are published through the moodle page of the course.
Prerequisites: As background, we require material taught in the course "252-0209-00L Algorithms, Probability, and Computing". It is not necessary that participants have actually taken the course, but they should be prepared to catch up if necessary.

Exams, Special Assignments and Grading

Grading: There will be a written exam in the examination session. Furthermore, there will be two mandatory written special assignments during the semester. The final grade of the whole course will be calculated as a weighted average of the grades for the exam (80%) and the special assignments (20%).
Special Assignments: At two times in the course of the semester, we will hand out specially marked exercises or term projects — the written part of the solutions are expected to be typeset in LaTeX or similar. Solutions will be graded, and the grades will account for 20% of the final grade. Assignments can be discussed with colleagues, but we expect an independent writeup.
Exam: Date to be determined. The exam lasts 120 minutes, it is written and closed-book. No written material permitted!

Regular Exercises

Theoretical Exercises

The theoretical exercises are discussed in classes. Students are expected to try to solve the problems beforehand. Your assistant is happy to look at your solutions and correct/comment them. We will assign students to classes according to surnames. Attendance according to these assignments is not compulsory but encouraged. The details of the classes are as follows.

Group Time Room Students with Surnames (Last Names) Assistant
A Tue 13-15 HG D3.2 A - L Yiming Yan
B Tue 13-15 HG D5.2 M - Z Saeed Ilchi

Practical Exercises

These form a self-study component which provides guidance to implement some of the methods discussed in the lectures. Students are encouraged to attempt these exercises and check against the suggested solutions, which will be made available online some time after the release of the exercises. Although they are not discussed in the regular classes, students can contact the practical exercise assistant (Hung Hoang) with any questions.