Hasso-Plattner-Institut20 Jahre HPI
Hasso-Plattner-Institut20 Jahre HPI
  
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Mathematics in Machine Learning (Sommersemester 2019)

Lecturer: Prof. Dr. Christoph Lippert (Digital Health & Machine Learning) , Matthias Kirchler (Digital Health & Machine Learning) , Dr. rer. nat. Stefan Konigorski (Digital Health & Machine Learning) , Orhan Konak (Digital Health - Personalized Medicine)

General Information

  • Weekly Hours: 4
  • Credits: 6
  • Graded: yes
  • Enrolment Deadline: 01.04.2019 bis 26.04.2019
  • Teaching Form: Lecture / Exercise
  • Enrolment Type: Compulsory Elective Module
  • Course Language: English

Programs & Modules

Digital Health MA
Data Engineering MA
  • DATA-Konzepte und Methoden
  • DATA-Techniken und Werkzeuge
  • DATA-Spezialisierung
IT-Systems Engineering MA

Description

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

 

16/07/2019

Final Exam

 

Linear Algebra

 

Calculus and Optimization

 

Probability

 

Advanced Topics

Examination

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.

Dates

  • 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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