Courses

Aktuelle Themen der Theoretischen Informatik I: Networks and high-dimensional inference

This course covers statistical and computational methods for understanding complex networks — from social platforms to biological systems. The central challenge it addresses is the inverse problem: inferring hidden network structure and interaction rules from indirect or incomplete observations.

Students learn to work with real-world networks that are noisy, partially observed, or entirely unobserved, drawing on tools from statistics, applied mathematics, computer science, and physics. Key outcomes include inferring latent structure, reconstructing interaction networks from time series data, and handling core difficulties like ill-posedness and underdetermination using Bayesian and information-theoretic frameworks.

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Information theory, inference, and learning algorithms

This course presents a unified treatment of information theory and statistical inference, highlighting their shared foundations and complementary perspectives, with emphasis on modern developments and interdisciplinary connections — particularly with statistical physics and theoretical computer science. Core topics include entropy and information measures, data compression and coding, the minimum description length principle, probabilistic graphical models, and inference algorithms such as belief propagation. By the end of the course, students will be able to apply core concepts such as entropy and mutual information to problems in statistical inference and learning, formulate inference problems within an information-theoretic and Bayesian framework, and model complex systems using probabilistic graphical models. Students will also develop an understanding of how ideas from statistical physics — such as free energy, entropy–energy tradeoffs, and phase transitions — illuminate the limits of inference and the emergence of computational hardness in high-dimensional systems.

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Networks and complex systems

This course provides a multidisciplinary introduction to the fundamentals of network analysis and the modeling of complex systems — systems consisting of many interacting components that give rise to emergent behaviors determined by, but not immediately predictable from, relatively simple interaction rules. Topics include elementary graph theory, random network models, network algorithms, characterization of network structure, network robustness, and dynamical processes on networks, drawing on theory and methods from diverse fields including graph theory, computer science, statistical physics, and information theory. The course also covers the statistical analysis of network data, which serves as a paradigmatic example of high-dimensional, interdependent data — a central challenge in modern data science. By the end of the course, students will be able to represent complex systems as networks and integrate theoretical models, algorithms, and real-world data to draw meaningful conclusions about their structure and behavior, identify the implications of different network architectures, compare and evaluate random network models for empirical systems, simulate and analyze dynamical processes on networks, and extract statistically significant information from empirical network data.

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Spatial Methods for Data Science

This course offers an interdisciplinary introduction to spatial data analysis, designed for students from natural and social sciences. It covers how systems of societal interest — from geographic and urban environments to political and social networks — can be understood through concepts of space, distance, and similarity. The curriculum is divided into two parts: the first examines methods for analysing physically embedded systems, such as spatial influence, flows, and pattern modelling, while the second extends these ideas into more abstract territory, exploring dimensionality reduction, embeddings, latent space models, and network geometry to uncover hidden structure in complex systems.

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Analytical Data Visualization

This praktikum introduces students to the principles and practice of analytical data visualization, motivated by the growing need to make sense of large, complex datasets across fields such as medicine, economics, environmental science, and engineering. While visualization is valuable both for exploratory analysis and for communicating findings to broader audiences, the core challenge across all domains is the same: transforming raw data into visual representations that are rigorous, intuitive, and meaningful. Rather than teaching fixed recipes, the course builds students’ understanding of what makes a visualization effective — drawing on visual perception, communication principles, and domain knowledge — and develops practical skills through hands-on work with real-world datasets using modern programming and visualization tools.

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