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-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 signal processing.

 

Course Syllabus and Schedule (Summer 2019)

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

 

CW / Week

Topic

15 / 1

Introduction

15 / 1

Introduction to Python Part I

16 / 2

Introduction to Python Part II

16 / 2

Basics

17 / 3

Random Variables, Joint distributions

17 / 3

Great Expectations

18 / 4

Variance, Covariance, Random Vectors

18 / 4

Estimation of Parameters, Gaussian distribution

19 / 5

Vector Spaces, Linear maps

19 / 5

Metric spaces, Normed Spaces, Inner Product Spaces

20 / 6

Eigenvalues, Eigenvectors, Trace, Determinant

20 / 6

Orthogonal matrices, Symmetric matrices

21 / 7

Positive (semi-)definite matrices

21 / 7

Singular value decompositions, Fundamental Theorem of Linear Algebra

22 / 8

Operator and matrix norms

22 / 8

Low-rank approximation

23 / 9

Pseudoinverses, Matrix identities

23 / 9

Extrema, Gradients, Jacobian, Hessian, Matrix calculus

24 / 10

Taylor's theorem, Conditions for local minima

24 / 10

Convexity

25 / 11

Convexity

25 / 11

Convexity

26 / 12

Signal decomposition

26 / 12

Fourier Transform

27 / 13

Fourier Transform

27 / 13

Wavelet Transform

28 / 14

 

28 / 14

Open Topics, Final Exam Preparation

29 / 15

 

29 / 15

Final Exam

 

Practical Knowledge

 

Linear Algebra

 

Calculus and Optimization

 

Probability

 

Signal Processing

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
  • Tutorials: Time and place will be discussed jointly with the students during the first lecture.

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