Gero Junike

Gero Junike, Marco Oesting

Neural networks are able to approximate any continuous function on a compact set. However, it is not obvious how to quantify the error of the neural network, i.e., the remaining bias between the function and the neural network. Here, we propose the application of extreme value theory to quantify large values of the error, which are typically relevant in applications. The distribution of the error beyond some threshold is approximately generalized Pareto distributed. We provide a new estimator of the shape parameter of the Pareto distribution suitable to describe the error of neural networks. Numerical experiments are provided.

Joris Dannemann, Gero Junike

Batch normalization is one of the most important regularization techniques for neural networks, significantly improving training by centering the layers of the neural network. There have been several attempts to provide a theoretical justification for batch ormalization. Santurkar and Tsipras (2018) [How does batch normalization help optimization? Advances in neural information rocessing systems, 31] claim that batch normalization improves initialization. We provide a counterexample showing that this claim s not true, i.e., batch normalization does not improve initialization.

Solveig Flaig, Gero Junike

In this research, we show how to expand existing approaches of using generative adversarial networks (GANs) as economic scenario generators (ESG) to a whole internal market risk model - with enough risk factors to model the full band-width of investments for an insurance company and for a one year time horizon as required in Solvency 2. We demonstrate that the results of a GAN-based internal model are similar to regulatory approved internal models in Europe. Therefore, GAN-based models can be seen as a data-driven alternative way of market risk modeling.