An analysis of Generative Adversarial Networks on lower dimensional spaces

Generative Adversarial Networks (GANs) provide a new way of generating data. In this thesis, a strictly controlled parameter space is introduced from which a sample space with known underlying distributions can be generated. Having exact knowledge of the underlying distributions of the parameter space, makes that we can evaluate the quality of the Generator, which is normally considered a hard task. We introduce an adapted version of the Wasserstein Distance (Earth-Movers distance) and use this along with the Inception score to evaluate the performance of the Generator. We evaluate different network types for the GAN, parameter spaces and GAN attributes (such as the number of input nodes and input distributions) on lower-dimensional samples (sine curves and Gaussian curves). To investigate the capabilities of a GAN to learn samples with low probability (extreme scenarios), we evaluate the capabilities of a Conditional GAN to generate in-sample data and out-of-sample data, since extreme scenarios are likely to be non-present in the training data. The results were that a GAN is able to interpolate learned concepts but performs badly in extrapolating. Having knowledge (or an expectation) of the true underlying distribution, a Weighted Sampling approach can be introduced to increase performance on low-probability samples.Financial institutions want to have the most accurate estimations of extreme scenarios one year ahead in time, to determine their capital requirements, and thus it is of high interest to estimate worst-case yield curves precisely. We considered US Treasury Zero-Coupon Bonds yield curves to evaluate if a GAN is able to support extreme scenario generation. A current practice to do so, which we consider the baseline, is a combination of a displaced log-transform, bootstrapping and Principal Component Analysis. We show that a Conditional GAN is able to learn the concepts of a US Treasury Zero-Coupon Bonds yield curve. However, a GAN is not able to generate the variety of one-year-ahead-in-time yield curves which the baseline approach does.Applied MathematicsComputer Scienc