Statistical analysis of Wasserstein GANs with applications to time series forecasting

• URL: http://arxiv.org/abs/2011.03074v1
• Date: Thu, 5 Nov 2020 19:45:59 GMT
• Title: Statistical analysis of Wasserstein GANs with applications to time series forecasting
• Authors: Moritz Haas, Stefan Richter
• Abstract summary: We provide statistical theory for conditional and unconditional Wasserstein generative adversarial networks (WGANs) We prove upper bounds for the excess Bayes risk of the WGAN estimators with respect to a modified Wasserstein-type distance. We formalize and derive statements on the weak convergence of the estimators and use them to develop confidence intervals for new observations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We provide statistical theory for conditional and unconditional Wasserstein generative adversarial networks (WGANs) in the framework of dependent observations. We prove upper bounds for the excess Bayes risk of the WGAN estimators with respect to a modified Wasserstein-type distance. Furthermore, we formalize and derive statements on the weak convergence of the estimators and use them to develop confidence intervals for new observations. The theory is applied to the special case of high-dimensional time series forecasting. We analyze the behavior of the estimators in simulations based on synthetic data and investigate a real data example with temperature data. The dependency of the data is quantified with absolutely regular beta-mixing coefficients.

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