# Mathematics for Machine Learning (Wintersemester 2020/2021)

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

## Allgemeine Information

• Semesterwochenstunden: 4
• ECTS: 6
• Benotet: Ja
• Einschreibefrist: 01.10.2020 -20.11.2020
• Lehrform: Vorlesung
• Belegungsart: Wahlpflichtmodul
• Lehrsprache: Englisch

## Studiengänge & Module

Data Engineering MA
IT-Systems Engineering MA
Digital Health MA

## Beschreibung

Both lectures and tutorials start in the second week only (i.e. from November 9th)!

Note that due to the online teaching format, there will be (asynchronous) online videos, but in exchange no lectures on Tuesdays (see format below)!

Course Moodle: https://hpi.de/friedrich/moodle/course/view.php?id=130
The course is also open to non-HPI students. If you don't have an HPI account to log into Moodle, send us a mail!

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 the context of machine learning. Beyond providing the solid mathematical foundation that is required for machine learning, we derive and discuss important machine learning concepts and algorithms.

 Topic Introduction Vector Spaces, Linear maps Metric spaces, Normed Spaces, Inner Product Spaces Eigenvalues, Eigenvectors, Trace, Determinant Orthogonal matrices, Symmetric matrices Positive (semi-)definite matrices Singular value decompositions, Fundamental Theorem of Linear Algebra Operator and matrix norms Low-rank approximation Pseudoinverses, Matrix identities Extrema, Gradients, Jacobian, Hessian, Matrix calculus Taylor's theorem, Conditions for local minima Gradient descent Second order methods Stochastic gradient descent Convexity Random Variables, Joint distributions Great Expectations Variance, Covariance, Random Vectors Estimation of Parameters, Gaussian distribution Frequentist vs. Bayesian Statistics Expectation Maximization Teaser in calculus of variations

## Voraussetzungen

Basic knowledge in Analysis/Calculus und Linear Algebra (equivalent to Bachelor lecture Mathematics II)

## Literatur

https://gwthomas.github.io/docs/math4ml.pdf

https://mml-book.github.io/

## Lern- und Lehrformen

Asynchronous lecture videos and exercise sessions via Zoom videoconferencing.

Materials and exercises will be managed over Moodle: https://hpi.de/friedrich/moodle/course/view.php?id=130
The course is also open to non-HPI students. If you don't have an HPI account to log into Moodle, send us a mail!

## Leistungserfassung

Written Exam at the end of the semester (100% of the grade).

Regular homework exercise sheets are required to be eligible for taking the exam (at least 50% of all points).

## Termine

Lectures & Tutorials will start in the second week only (i.e. November 9th and November 11th)!

Lectures:

Contrary to the timetable, there will be no lecture on Tuesdays, but instead videos with the material (link on moodle).
Lectures on Wednesdays 9:15-10:45 will be held over Zoom (link on moodle) and be in a Q&A style, discussing the topics of the week.

Tutorials:

Mondays, 9:00 - 10:30 over Zoom (link on moodle)

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