# Mathematics for Machine Learning (Wintersemester 2021/2022)

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

## General Information

• Weekly Hours: 4
• Credits: 6
• Teaching Form: Lecture
• Enrolment Type: Compulsory Elective Module
• Course Language: English

## Programs & Modules

Data Engineering MA
• DATA-Konzepte und Methoden
• DATA-Techniken und Werkzeuge
• DATA-Spezialisierung
IT-Systems Engineering MA
Digital Health MA

## Description

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

## Requirements

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

## Literature

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

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

## Learning

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!

## Examination

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).

## Dates

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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