Mathematics in Machine Learning (Sommersemester 2019)

Dozent: Prof. Dr. Christoph Lippert (Digital Health - Machine Learning) , Matthias Kirchler (Digital Health - Machine Learning) , Dr. rer. nat. Stefan Konigorski (Digital Health - Machine Learning)

Allgemeine Information

• Semesterwochenstunden: 4
• ECTS: 6
• Benotet: Ja
• Einschreibefrist: 01.04.2019 bis 26.04.2019
• Lehrform: Vorlesung / Übung
• Belegungsart: Wahlpflichtmodul
• Lehrsprache: Englisch

Studiengänge, Modulgruppen & Module

Beschreibung

Machine learning uses tools from a variety of mathematical fields.

During this applied mathematics course, we cover a summary of the mathematical tools from linear algebra, calculus, optimization and probability theory that are commonly used in machine learning. This part provides a solid mathematical foundation for an introductory class in machine learning, such as the course “Machine Learning in Precision Medicine”, offered in parallel. We will introduce further mathematical aspects related to machine learning, including optimization, as well as information theory.

 

Course Syllabus and Schedule (Summer 2019)

Note that the syllabus and schedule are preliminary and maybe subject to change.

Date	Topic
08/04/2019	Introduction
09/04/2019	Random Variables, Joint distributions
15/04/2019	Great Expectations
16/04/2019	Variance, Covariance, Random Vectors
22/04/2019	Ostern
23/04/2019	Estimation of Parameters, Gaussian distribution
29/04/2019	Bayesian Inference
30/04/2019	Vector Spaces, Linear maps
06/05/2019	Metric spaces, Normed Spaces, Inner Product Spaces
07/05/2019	Eigenvalues, Eigenvectors, Trace, Determinant
13/05/2019	Orthogonal matrices, Symmetric matrices
14/05/2019	Positive (semi-)definite matrices
20/05/2019	Singular value decompositions, Fundamental Theorem of Linear Algebra
21/05/2019	Operator and matrix norms
27/05/2019	Low-rank approximation
28/05/2019	Pseudoinverses, Matrix identities
03/06/2019	Extrema, Gradients, Jacobian, Hessian, Matrix calculus
04/06/2019	Taylor's theorem, Conditions for local minima
10/06/2019	Pfingsten
11/06/2019	Gradient descent
17/06/2019	Second order methods
18/06/2019	Stochastic gradient descent
24/06/2019	Convexity
25/06/2019	Information Theory 1
01/07/2019	Information Theory 2
02/07/2019	Teaser in calculus of variations
08/07/2019
09/07/2019	Open Topics, Final Exam Preparation
15/07/2019
22/07/2019	Final Exam at 10am in HE.51/52

	Linear Algebra
	Calculus and Optimization
	Probability
	Advanced Topics

Leistungserfassung

The final grade is based 100% on the final written exam.

Processing of regular exercise sheets (every one to two weeks) is required for a Klausur approval.

Termine

• Lecture #1:  Monday 9:15-10:45
• Lecture #2: Tuesday 13:30-15:00
• Place: Lecture Hall 3 (HPI Campus I / Hörsaalgebäude)
• Tutorials: Time and place will be discussed jointly with the students during the first lecture.

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