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

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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