Mathematics for Machine Learning (Wintersemester 2021/2022)

Dozent: Prof. Dr. Christoph Lippert (Digital Health - Machine Learning) , Dr. Masoumeh Javanbakhat (Digital Health - Machine Learning) , Tahir Miriyev (Digital Health - Machine Learning)

Allgemeine Information

• Semesterwochenstunden: 4
• ECTS: 6
• Benotet: Ja
• Einschreibefrist: 01.10.2021 -22.10.2021
• Lehrform: Vorlesung
• Belegungsart: Wahlpflichtmodul
• Lehrsprache: Englisch

Studiengänge, Modulgruppen & Module

Beschreibung

We will start the course in the second week only 11/03/2021

Note that there will be (asynchronous) online videos provided, followed by the Tuesday excercises and debriefings on Wednedays!

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.

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 exercise sessions via Zoom videoconferencing.

Materials and exercises will be managed over Moodle: https://moodle.hpi.de/course/index.php?categoryid=65.
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

The course will start in the second week only (from 03 November 2021)

 

Lectures:
videos with the lecture & material will be provided on moodle.
Debriefing on Wednedays from 9:15am will be held over Zoom (link on moodle) and be in a Q&A style, discussing the topics of the week.
Depending on the regulations and the pandemic situation, we can also hold the meeting on site in HS 2.

Tutorials:
Tuesdays, from 9:15am (from 09 November 2021)

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