[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.