# Mathematics for Machine Learning (Wintersemester 2022/2023)

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

## Allgemeine Information

• Semesterwochenstunden: 4
• ECTS: 6
• Benotet: Ja
• Einschreibefrist: 01.10.2022 -31.10.2022
• Prüfungszeitpunkt §9 (4) BAMA-O: 20.02.2023
• Lehrform: Vorlesung
• Belegungsart: Wahlpflichtmodul
• Lehrsprache: Englisch

## Studiengänge, Modulgruppen & Module

IT-Systems Engineering MA
• OSIS: Operating Systems & Information Systems Technology
• HPI-OSIS-K Konzepte und Methoden
• OSIS: Operating Systems & Information Systems Technology
• HPI-OSIS-T Techniken und Werkzeuge
Digital Health MA
Data Engineering MA
Software Systems Engineering MA

## Beschreibung

Course Moodle: will be made available shortly
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. At the end of this course students would be able to understand the under the hood of machine learning algorithms, going through the research papers and understand the deep learning books.

 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 plus debriefings and weekly exercise sessions in person. Some of the in-person sessions might be replaced by online sessions.

## 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).

Exam: 02/20/2023 from 9am in L-E.03

## Termine

The course will start on October 24th.

Lectures:
videos with the lecture & material will be provided on moodle.
Debriefing on Mondays from 9:15am will be held in person (L-E.03) or over Zoom (link on moodle) and be in a Q&A style, discussing the topics of the week.

Tutorials:
Tuesdays, from 9:15am (L-E.03)

Exam
Monday, 02/20/2023 from 9am in L-E.03

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