Hasso-Plattner-Institut25 Jahre HPI
Hasso-Plattner-Institut25 Jahre HPI

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

IT-Systems Engineering MA
Data Engineering MA
Digital Health MA
  • SCAD: Scalable Computing and Algorithms for Digital Health
    • HPI-SCAD-C Concepts and Methods
  • SCAD: Scalable Computing and Algorithms for Digital Health
    • HPI-SCAD-T Technologies and Tools
  • SCAD: Scalable Computing and Algorithms for Digital Health
    • HPI-SCAD-S Specialization
  • APAD: Acquisition, Processing and Analysis of Health Data
    • HPI-APAD-C Concepts and Methods
  • APAD: Acquisition, Processing and Analysis of Health Data
    • HPI-APAD-T Technologies and Tools
  • APAD: Acquisition, Processing and Analysis of Health Data
    • HPI-APAD-S Specialization
Software Systems Engineering MA


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.

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
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


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





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


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


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.

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