Probabilistische Techniken und Algorithmen in der Datenanalyse

What it is about

You will learn probabilistic techniques and algorithms used in data analysis for dimensionality reduction and data recovery from incomplete information. In the end, you will understand the basics of random matrices, assess randomized algorithms, and apply and analyze methods such as JL embeddings, compressed sensing, and randomness-based matrix/tensor reconstruction.

What you will be able to do

• Understand the theory and properties of random variables and random matrices
• Apply concentration inequalities and covering arguments
• Analyze reconstruction guarantees in compressed sensing
• Understand low-rank reconstruction for matrices and tensors
• Construct and evaluate Johnson–Lindenstrauss embeddings
• Evaluate randomized algorithms for large datasets
• Apply probabilistic models for clustering and random subspaces

What the module consists of

• VorlesungConveying the content through lecture and discussion
• ÜbungGuided and increasingly independent practice on case studies and exercises, also in small groups

Teaching method

• Vortrag und Diskussionto convey the theoretical content and to stimulate reading of the literature
• Übungsaufgaben und Fallbeispieleto practice and apply the competencies, increasingly independently