Selection of courses offered in WS 2024/2025
[Lecture] Advanced Machine Learning
In the Advanced Machine Learning lecture we will cover various advanced concepts, techniques, and algorithms. We will place focus both on the mathematical and theoretical aspects, as well as the practical aspects which involve implementing, training, and optimizing machine learning models using real-world datasets. The lecture is organized in four parts. In the first part we will tackle machine learning for graph data including generative models, ranking, and graph neural networks. In the second part we will cover modern generative models such as variational autoencoders, normalizing flows and generative adversarial networks. In the third part we will cover robustness including both attacks on machine learning models (evasion, poisoning) and defenses (certificates). Finally, in the last part we will cover uncertainty quantification techniques such as Bayesian neural networks, Gaussian processes and conformal prediction.
[Lecture] Scientific Machine Learning
Scientific Machine Learning is a new research area that is developing as a field of its own, in which techniques of scientific computing and machine learning are combined and further developed. This results in hybrid methods that are applied to the discretization of partial differential equations, the development of fast and robust solvers, and new modeling techniques.
Keywords are
- Domain-aware scientific machine learning,
- Mathematics-informed machine learning,
- Interpretable scientific machine learning,
- Machine learning-enhanced simulations,
- Hybrid modeling (machine learning + first principle modeling).
[Seminar] Adversarial Machine Learning
In the Adversarial Machine Learning seminar, we will explore the robustness of machine learning models. This seminar will have a practical focus where the students will be split into two sets of teams. One set of teams will focus on developing various attacks to break or manipulate machine learning models, e.g. given an image of a cat design algorithms to add impercetible adversarial noise to the input to cause the model to misclassify it as a dog. The other set of teams will focus on defending against such attacks. The attacks and defenses will be carried out in multiple rounds allowing the attackers and defenders to learn from each other to improve their approach.
[Seminar] Machine Learning methods to predict individual differences with Python
This course will start with learning the basics of programming in Python, so no prior programming knowledge is needed, but helpful. Next will be an introduction to data handling and visualization (i.e., with Seaborn, matplotlib). After that, we will start with basic concepts used in machine learning (i.e., learning, prediction) and helpful methodologies (i.e., cross-validation to prevent overfitting). In the final part of the course, we will learn to apply several machine-learning procedures (i.e., regressions, tree models, deep-learning) and to use model explainers to allow the interpretation of results from otherwise black-box models. As software tools, we will use Jupyther/Colab notebooks. Miniconda or Anaconda should be installed, but all software is freely available. Depending on student demand, this course can be held in German.
[Seminar] Methods of Mathematical Modeling in Life Sciences
The seminar will discuss recent work on applications of mathematical modeling in the life sciences. The focus is on current developments of machine learning and artificial intelligence methods for industrial problems in the fields of pharmaceuticals and agricultural sciences. This seminar discusses different aspects, such as the mathematical methodology behind each method, its computational complexity, and possible applications. In individual cases, publicly available methods will also be applied and the results discussed.
[Seminar] Theory of Machine Learning
In this seminar, the theoretical and algorithmic basics of machine learning are covered. Individual chapters from the book Shai Shalev-Shwartz, Shai Ben-David, Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, are discussed.
[Seminar] Programming Competition: Modeling of Climate Change Scenarios
In this module you take part in a programming competition about the modeling of risks of climate change. A regression function fed with public weather data needs to be implemented. Likely, the output will be publicly available mortality data. If other reliable data is available, it will be used as well.
The participants can additionally take part with their contribution in a competition sponsored by a business consultancy. The details will be made available at the beginning of the semester; the participation in the competition is voluntary, and it does not require an additional programming effort. The participants' works for the seminar are scored independently of the competition.
Expected skills:
• Good programming skills in Python, Java, or R. (There won't be enough time to acquire these skills during the semester.)
• Interest in the topic of the programming competition
• Work independently to process public data and experiment with various Machine Learning models
• Interest in Data Science
• Helpful are first experiences with Machine Learning models such as neural networks and decision trees.
The goal is to model the impact of climate changes (particularly the temperature) on human health and mortality.
[Seminar] Selected Topics in Convex Optimization
Potential topics include convex optimization for computer-assisted proofs and algorithms, as well as machine learning techniques for quantifier elimination in real closed fields. Prerequisites for this seminar are the lectures "Polynomial Optimization" or "Convex Optimization".
[Seminar] Seminar for Teachers at Grammar and Comprehensive Schools: Practical Algorithms for Instruction
The seminar is targeted at student teachers who are interested in a realistic, youth-oriented teaching structure for the high school level through algorithms in the context of different applications like MP3, JPEG, RSA, GPS, the computation of the Page Rank by search engines etc.
In line with the topic of the Year of Science 2019 (an initiative of the Federal Ministry of Education and Research in Germany), algorithms from the area of artificial intelligence (AI) and machine learning (ML) are treated. Quantum computing and quantum algorithms are another possible focus for the seminar.
For the algorithms and mathematical models, teaching modules are supposed to be created that can supplement the current curricula. The lectures will present the corresponding mathematical basics and a suitable didactic concept.
[Seminar] Inference and Machine Learning for Scientific Research
This seminar shall give an introduction to modern methods of data analysis and machine learning for scientific research. We will focus on methods beyond “black box models” that allow for scientific insight and discoveries.
Contents of the course:
• Fundamentals of Data Analysis and Machine Learning
• Bayesian Statistics and Data Analysis
• Interpretable Machine Learning
• Causal Inference and Modelling
• Inference of Nonlinear Dynamic Systems and Networks
Selection of courses offered in SS 2024
[Lecture] Machine Learning
This course introduces students to the fundamental concepts, techniques, and algorithms in machine learning. It covers the mathematical and theoretical foundations, supervised and unsupervised learning techniques, evaluation methods, and advanced aspects. Students will gain hands-on experience in implementing, training, and optimizing machine learning models using real-world datasets.
The tentative list of topics is as followed:
- Introduction
- Probabilistic Inference
- Trees and Forests
- Neighbor-based methods
- Linear models
- (Convex) Optimization
- Gradient-based Optimization
- SVMs
- Kernels
- Basics of Deep Learning: MLPs, CNNs, GNNs
- Dimensionality Reduction: PCA & tSNE
- SVD & Matrix Factorization
- k-Means and GMMs
- Hierarchical Clustering
- Robustness
- Uncertainty
- Privacy
- Fairness
[Lecture] Mathematics of Data Science – An Introduction
As the importance and widespread use of automated simulations, decision-making processes and AI continues to grow, new challenges arise in the analysis and processing of data. In particular, the growing complexity of tasks and the available size of the data sets used for the above-mentioned areas require new and more efficient approaches from the fields of data science, data mining, and machine learning in general.
This lecture will cover theoretical and algorithmic foundations of modern data processing and analysis. The lecture is strongly, but not exclusively, based on the literature listed below and covers the following topics, among others:
- Techniques for dimension reduction (singular value decomposition/PCA/robust PCA)
- Classical regression
- Clustering algorithmsClassification using Support Vector Machines and Linear Discriminant Analysis
- Classification using Classification Trees and Random Forest
- Classical neural networks or introduction to deep learning
- Introduction to Reinforcement Learning (optional)
- Reduced Order Models (ROMs) (optional)
The lecture will have a strong focus on the algorithmics and mathematical computability of the methods mentioned as well as the application-oriented implementation and less on statistical methods, which are also a component of data science.
Brunton, S., & Kutz, J. (2022). Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (2nd ed.). Cambridge: Cambridge University Press. doi:10.1017/9781009089517
[Seminar] Trustworthy Machine Learning
Machine learning models are increasingly used in safety-critical applications and to make automated decisions about humans. Beyond accuracy and efficiency, we expect such models to also be robust to noise and adversaries, to faithfully represent their (aleatoric and epistemic) uncertainty, to preserve privacy, to be fair w.r.t. different demographic groups, and to be interpretable. In this seminar, we will cover the latest research on these trustworthiness aspects, as well as the (fundamental) trade-offs between them. We will study the shortcomings and failures of traditional machine learning models and how to improve them.
[Seminar] Methods of Mathematical Modeling in Life Sciences
The seminar will discuss recent work on applications of mathematical modeling in the life sciences. The focus is on current developments of machine learning and artificial intelligence methods for industrial problems in the fields of pharmaceuticals and agricultural sciences. This seminar discusses different aspects, such as the mathematical methodology behind each method, its computational complexity, and possible applications. In individual cases, publicly available methods will also be applied and the results discussed.
[Seminar] Machine Learning
In this seminar, we will discuss machine learning methods currently used in various application areas. We will focus on concrete methods, for example:
• mathematical basics,
• model-selection algorithms,
• regularization,
• dimension reduction,
• decision trees,
• support vector machines,
• neural networks.
The basis for the seminar is the book “The Elements of Statistical Learning”.
[Practical Course] Interactive Visualization in Research and Application
This seminar uses current research for practical applications of information visualization. The topics cover the areas of visual design, using machine learning in visualization, interaction, evaluation of visualization techniques or their application. The goal of the seminar is to learn to work through and understand scientific works and use them for own practical applications.
Selection of courses offered in WS 2023/2024
[Lecture] Advanced Machine Learning
In the lecture we will cover various advanced machine learning concepts, techniques, and algorithms. We will place focus both on the mathematical and theoretical aspects, as well as the practical aspects which involve implementing, training, and optimizing machine learning models using real-world datasets. Some of the topics that we will cover include: semi-supervised learning, machine learning for graph data, machine learning for sequential data, Gaussian processes, temporal point processes, trustworthy machine learning, advanced topics in optimization, machine learning theory, and generative models.
[Lecture] Deep Learning
New developments in the field of deep neural networks have enabled a large amount of applications in recent years that were previously unthinkable to achieve in high quality: From image recognition, speech recognition, simulation of protein folding, automatic playing of computer games to image generation or speech generation with systems like ChatGPT. In this lecture we will cover the concepts behind deep neural networks, in particular Convolutional Neural Networks, attention mechanisms, modern transformer architectures, and their extensions. We focus on supervised deep learning and unsupervised deep learning, where many training examples are available for a given task, and the network learns independently from this data. In this lecture, a mathematical understanding of the mechanisms and the design of neural networks is conveyed. At the same time, examples are given on how to efficiently implement and use neural networks with the help of modern Deep Learning frameworks such as PyTorch.
[Lecture] Scientific Machine Learning
Scientific Machine Learning is a new research area that is developing as a field of its own, in which techniques of scientific computing and machine learning are combined and further developed. This results in hybrid methods that are applied to the discretization of partial differential equations, the development of fast and robust solvers, and new modeling techniques.
Keywords are
- Domain-aware scientific machine learning,
- Mathematics-informed machine learning,
- Interpretable scientific machine learning,
- Machine learning-enhanced simulations,
- Hybrid modeling (machine learning + first principle modeling).
[Seminar] On Applications in Life Sciences
The seminar will discuss recent work on applications of mathematical methods in the life sciences. The focus is on current developments of machine learning and artificial intelligence methods for industrial problems in the fields of pharmaceuticals and agricultural sciences. This seminar discusses different aspects, such as the mathematical methodology behind each method, its computational complexity, and possible applications. In individual cases, publicly available methods will also be applied and the results discussed.
[Seminar] Machine Learning
In this seminar, we will discuss machine learning methods currently used in various application areas. We will focus on concrete methods, for example:
• mathematical basics,
• model-selection algorithms,
• regularization,
• dimension reduction,
• decision trees,
• support vector machines,
• neural networks.
The basis for the seminar is the book “The Elements of Statistical Learning”.
[Seminar] Theory of Machine Learning
In this seminar the theoretical and algorithmic basics of machine learning will be treated. Individual chapters from the book “Understanding Machine Learning: From Theory to Algorithms” are discussed.
[Practical Course] Applied Visual Analytics
The practical training deals with the design, implementation and evaluation of visual analysis of large and complex data sets: Visualization, interaction, human perception, data analysis and their combination to solve application-oriented problems. Problems from current research and application topics in the field of visual analytics will be addressed and implemented. Application areas are for example finance, economics, geosciences, meteorology, medicine, biology, transportation, or sports. In addition to deepening technical knowledge, the course can also be used to acquire communication and presentation skills.