Project 03: Mathematical Foundations of Bayesian Neural Networks
03 Mathematical Foundations of Bayesian Neural Networks
MATH PI: TT-Prof. Dr. Sebastian Krumscheid, Steinbuch Centre for Computing (SCC), Junior Research
Group Uncertainty Quantification (SCC-UQ) & Institute for Applied and Numerical Mathematics
SEE PI: Dr. Charlotte Debus, Steinbuch Centre for Computing (SCC), Junior Research Group Robust
and Efficient AI (SCC-RAI)
Department(s): Mathematics or Informatics (Computer Science)
Type of position: 75% FTE, TV-L E13
With the increasing application of machine learning (ML) methods, the robustness of such data-driven
methods becomes a central aspect. Modern ML models must not only be able to deliver
unprecedented prediction accuracy but are also required to deliver an estimate of the uncertainty of
that prediction. Assessing the possible error margin on a prediction is essential in applying ML models
to critical infrastructures, such as electricity resource planning from renewable energy sources.
For deep learning (DL), Bayesian Neural Networks (BNN) provide a promising approach to quantifying
the inherent data uncertainty and that of the ML model itself, which arises from the optimization
process. However, currently available theoretical approaches and their practical implementations of
BNNs need to be improved, particularly regarding computational efficiency and the accurate
description of uncertainties.
Addressing these shortcomings is the aim of this doctoral project. Specifically, the overarching goal is
to expand the mathematical theory behind variational inference underpinning Bayesian neural
networks to provide accurate and computationally efficient model uncertainties. Situated at the
intersection of mathematics and computer science, this doctoral project combines statistical methods
and Bayesian theory with state-of-the-art deep learning approaches. The methods developed in the
context of this project will be evaluated on the use-case of predicting photovoltaic electricity
generation, which is relevant for optimal scheduling of electricity allocation.
Requirements for this position:
- A degree (M.Sc. or equivalent) in computer science, mathematics or another related field, e.g.
physics or engineering.
- Basic knowledge of and initial experience with machine learning methods, preferably in Deep
- Basic knowledge of applied mathematics, including numerical analysis, statistics, and Bayesian
- Solid programming skills in any scientific programming language, such as Python, C/C++
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