Mathematics for Machine Learning (Sommersemester 2024)

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

Allgemeine Information

• Semesterwochenstunden: 4
• ECTS: 6
• Benotet: Ja
• Einschreibefrist: 01.04.2023 - 30.04.2023
• Lehrform: Vorlesung
• Belegungsart: Wahlpflichtmodul
• Lehrsprache: Englisch

Studiengänge, Modulgruppen & Module

Beschreibung

NOTE:The course starts on Tuesday, April 09 3:15pm

Course Moodle: https://moodle.hpi.de/course/view.php?id=769
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!

We encourage participation in-person. As the course is also open to students at the Icahn School of Medicine at Mount Sinai, we provide a Zoom link on the Moodle page.

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/

Leistungserfassung

Written Exam at the end of the semester (70% of the grade). The remaining 30% of the grade will be based on a python project, where you will implement a new machine learning algorithm.

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

Exam: date tbd

Termine

The course starts on Tuesday, April 09 3:15pm

Lectures:

A typical week looks as follows:
Mondays at 17:00 - 18:30: Interactive pen and paper lectures in room G3.E15/16. The goal is to apply the learned mathematical tools to derive and analyze a new machine learning method.

Tuesdays between 15:15 - 16:45:  Computer implementation lecture in room G3.E15/16. We will implement the new machine learning methods in python using numpy and apply them to various data sets.
The rest of the week: watch the lecture videos and finalize any unfinished tutorial exercises.

Grading
The grade will be 70% based on a written exam and 30% based on a python project.

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