This lecture introduces to the main mathematical concepts underpinning the field of data science, with emphasis on the algorithmic exposition and the main theoretical results from numerics.
The lecture will cover the following topics:
- Introduction to parameter optimization problems and neural networks
- Numerical linear algebra: Matrix decompositions, QR decomposition, singular value decomposition
- Optimization methods: Gradient descent, stochastic gradient descent, Adam algorithm
- Automatic differentiation
- High-performance, hardware-aware programming with GPUs
- Software concepts for machine learning (tensorflow/pytorch)
Learning goals:
Upon successful completion of the course, the students will be familiar with the main algorithms for numerical data science. Their knowledge will enable them to translate practical data science problems into the language of mathematics and select appropriate algorithms for their solution. The students will have the knowledge of the complexities and capabilities of hardware-oriented implementations in the field of machine learning, and are able to implement solutions for a range of problems in data science in modern software.
- Kursleiter/in: Katharina Kormann
- Kursleiter/in: Martin Kronbichler