Analytical Description of Variational Autoencoders and Application of Temporal Variational Autoencoders to Financial Risk Management
- An increasing number of nowadays tasks, such as speech recognition, image generation,
translation, classification or prediction are performed with the help of machine learning.
Especially artificial neural networks (ANNs) provide convincing results for these tasks.
The reasons for this success story are the drastic increase of available data sources in
our more and more digitalized world as well as the development of remarkable ANN
architectures. This development has led to an increasing number of model parameters
together with more and more complex models. Unfortunately, this yields a loss in the
interpretability of deployed models. However, there exists a natural desire to explain the
deployed models, not just by empirical observations but also by analytical calculations.
In this thesis, we focus on variational autoencoders (VAEs) and foster the understanding
of these models. As the name suggests, VAEs are based on standard autoencoders (AEs)
and therefore used to perform dimensionality reduction of data. This is achieved by a
bottleneck structure within the hidden layers of the ANN. From a data input the encoder,
that is the part up to the bottleneck, produces a low dimensional representation. The
decoder, the part from the bottleneck to the output, uses this representation to reconstruct
the input. The model is learned by minimizing the error from the reconstruction.
In our point of view, the most remarkable property and, hence, also a central topic
in this thesis is the auto-pruning property of VAEs. Simply speaking, the auto-pruning
is preventing the VAE with thousands of parameters from overfitting. However, such a
desirable property comes with the risk for the model of learning nothing at all. In this
thesis, we look at VAEs and the auto-pruning from two different angles and our main
contributions to research are the following:
(i) We find an analytic explanation of the auto-pruning. We do so, by leveraging the
framework of generalized linear models (GLMs). As a result, we are able to explain
training results of VAEs before conducting the actual training.
(ii) We construct a time dependent VAE and show the effects of the auto-pruning in
this model. As a result, we are able to model financial data sequences and estimate
the value-at-risk (VaR) of associated portfolios. Our results show that we surpass
the standard benchmarks for VaR estimation.