Hasso-Plattner-InstitutSDG am HPI
Hasso-Plattner-InstitutDSG am HPI
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Mathematics for Machine Learning (Wintersemester 2022/2023)

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

General Information

  • Weekly Hours: 4
  • Credits: 6
  • Graded: yes
  • Enrolment Deadline: 01.10.2022 -31.10.2022
  • Teaching Form: Lecture
  • Enrolment Type: Compulsory Elective Module
  • Course Language: English

Programs, Module Groups & Modules

IT-Systems Engineering MA
  • OSIS: Operating Systems & Information Systems Technology
    • HPI-OSIS-K Konzepte und Methoden
  • OSIS: Operating Systems & Information Systems Technology
    • HPI-OSIS-T Techniken und Werkzeuge
Digital Health MA
Data Engineering MA
Software Systems Engineering MA

Description

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

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 weekly exercise sessions in person. Some of the in-person sessions might be replaced by online sessions.

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 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)

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