This course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in data science.
Lernziel
Understanding the theoretical guarantees (and their limits) of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science.
Inhalt
This course provides an in-depth theoretical treatment of optimization methods that are particularly relevant in machine learning and data science.
In the first part of the course, we will first give a brief introduction to convex optimization, with some basic motivating examples from machine learning. Then we will analyse classical and more recent first and second order methods for convex optimization: gradient descent, projected gradient descent, subgradient descent, stochastic gradient descent, Nesterov's accelerated method, Newton's method, and Quasi-Newton methods. The emphasis will be on analysis techniques that occur repeatedly in convergence analyses for various classes of convex functions. We will also discuss some classical and recent theoretical results for nonconvex optimization.
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.
Voraussetzungen / Besonderes
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.
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Die Leistungskontrolle wird nur in der Session nach der Lerneinheit angeboten. Die Repetition ist nur nach erneuter Belegung möglich.
Prüfungsmodus
schriftlich 120 Minuten
Zusatzinformation zum Prüfungsmodus
At two times in the course of the semester, we will hand out specially marked exercises or term projects (compulsory continuous performance assessments) - 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.
Hilfsmittel schriftlich
Keine
Diese Angaben können noch zu Semesterbeginn aktualisiert werden; verbindlich sind die Angaben auf dem Prüfungsplan.
Leistungskontrolle als Semesterkurs