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
- Prüfungszeitpunkt §9 (4) BAMA-O: 16.07.2024
- Lehrform: Vorlesung
- Belegungsart: Wahlpflichtmodul
- Lehrsprache: Englisch
Studiengänge, Modulgruppen & Module
- OSIS: Operating Systems & Information Systems Technology
- HPI-OSIS-K Konzepte und Methoden
- OSIS: Operating Systems & Information Systems Technology
- HPI-OSIS-T Techniken und Werkzeuge
- DANA: Data Analytics
- HPI-DANA-K Konzepte und Methoden
- DANA: Data Analytics
- HPI-DANA-T Techniken und Werkzeuge
- DANA: Data Analytics
- HPI-DANA-S Spezialisierung
- 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
- MALA: Machine Learning and Analytics
- HPI-MALA-C Concepts and Methods
- MALA: Machine Learning and Analytics
- HPI-MALA-T Technologies and Tools
- HPI-SSE-C Conceptual Foundations
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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