Teaching - Mathematical Algorithmic Optimization

Lecture: Optimization Methods for Machine Learning

The lecture (LSF) will be taught in English and addresses Master and PhD students in Mathematics or related fields. We will discuss the format in our first meeting. Slides of the lectures and videos of lectures are available.

Exercises and Downloads

The main resource of videos, pdfs, and exercise material is this website that you can access with a password provided in the lecture.

Information

Lecture with 4+2 SWS and 9 ECTS-Credits
Lectures: Mon 11h15-12h45 (G05-211) and Tue 13h15-14h45 (G03-214)
Practical exercises: Thu 13h15-14h45 (G05-118)
Lecturer practical exercises

Content

It will survey optimization problems in and methods for machine learning. Table of contents:

Introduction to Machine Learning
Machine Learning Case Studies: text classification and perceptual tasks
Problem Definitions and Methods Overview
Efficient Calculation of Derivatives
Problem reformulations
Stochastic Gradient Methods
Noise Reduction Methods
Second-Order Methods
Other Popular Methods
Ethical, Philosophical, and Economical Aspects of Artifical Intelligence

Practical exercises will complement the lecture and focus on KERAS and Python scikit-learn.

Requirements

Mathematical basics (Analysis and Linear Algebra) and programming skills. Introduction to Optimization. The lecture Nonlinear Optimization is highly recommended, but not absolutely necessary.

Module description

The lecture is a master lecture in the mathematics curriculum and described in the module handbook (currently page 31) as a Wahlpflicht module:

WPF MA (Module 12, 13, 14)
WPF MA;M 1-3 (Module M3D)

A translation of the module description:

Goals and competences: The students acquire competences with respect to modeling and algorithmically solving optimization problems that are at the basis of modern machine learning techniques. A rigorous mathematical analysis of convergence theory and implementation aspects of different algorithms is the guiding theme of the lecture. In the exercises the students learn how to implement algorithms efficiently on a computer and to apply them to concrete problem instances.
Content: An introduction to mathematically formulating machine learning problems in a generalized way, calculating derivatives, stochastic and deterministic derivative-based algorithms, convergence theory. See above for a table of contents.

The lecture is also open to other master and PhD students of OVGU. In particular, there is an agreement that ORBA students may choose the lecture as a Wahlpflicht (with 10 CP to motivate the independent study of mathematical foundations necessary to follow the lecture). However, please note that the lecture is addressed to mathematical master students and assumes a good understanding of mathematical basics, especially in the second part of the lecture. If you are mainly interested in applying machine learning and not so much in analyzing the training process, other lectures might be better suited for you. Note that the lecture Concepts and Algorithms of Optimization is not sufficient as a requirement, you will have to invest more time to acquire additional mathematical knowledge.