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.
Department of Mathematics（数学系）；Computer Vision Laboratory（计算机视觉实验室）；Department of Information Technology and Electrical Engineering（信息技术与电气工程系）
The extension of image generation to video generation turns out to be a very difficult task, since the temporal dimension of videos introduces an extra challenge during the generation process. Besides, due to the limitation of memory and training stability, the generation becomes increasingly challenging with the increase of the resolution/duration of videos. In this work, we exploit the idea of progressive growing of Generative Adversarial Networks (GANs) for higher resolution video generation. In particular, we begin to produce video samples of low-resolution and short-duration, and then pro…
Insight Centre for Data Analytics（洞察数据分析中心）；Dublin City University（都柏林城市大学）
In the recent years Generative Adversarial Networks (GANs) have demonstrated significant progress in generating authentic looking data. In this work we introduce our simple method to exploit the advancements in well established image-based GANs to synthesise single channel time series data. We implement Wasserstein GANs (WGANs) with gradient penalty due to their stability in training to synthesise three different types of data; sinusoidal data, photoplethysmograph (PPG) data and electrocardiograph (ECG) data. The length of the returned time series data is limited only by the image resolution, …
Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）
We introduce the decision-aware time-series conditional generative adversarial network (DAT-CGAN) as a method for time-series generation. The framework adopts a multi-Wasserstein loss on structured decision-related quantities, capturing the heterogeneity of decision-related data and providing new effectiveness in supporting the decision processes of end users. We improve sample efficiency through an overlapped block-sampling method, and provide a theoretical characterization of the generalization properties of DAT-CGAN. The framework is demonstrated on financial time series for a multi-time-st…
Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions. Motivated by such data, we propose an autoregressive model for density time series by exploiting the tangent space structure on the space of distributions that is induced by the Wasserstein metric. The densities themselves are not assumed to have any specific parametric form, leading to flexible forecasting of future unobserved densities. The main estimation targets…
Generative adversarial networks (GANs) are recently highly successful in generative applications involving images and start being applied to time series data. Here we describe EEG-GAN as a framework to generate electroencephalographic (EEG) brain signals. We introduce a modification to the improved training of Wasserstein GANs to stabilize training and investigate a range of architectural choices critical for time series generation (most notably up- and down-sampling). For evaluation we consider and compare different metrics such as Inception score, Frechet inception distance and sliced Wasser…
We propose a family of relaxations of the optimal transport problem which regularize the problem by introducing an additional minimization step over a small region around one of the underlying transporting measures. The type of regularization that we obtain is related to smoothing techniques studied in the optimization literature. When using our approach to estimate optimal transport costs based on empirical measures, we obtain statistical learning bounds which are useful to guide the amount of regularization, while maintaining good generalization properties. To illustrate the computational ad…
Google DeepMind（谷歌DeepMind）；CoMPLEX, Computer Science, UCL（伦敦大学学院计算生命科学中心，计算机科学系）；Google（谷歌）
The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying geometry between outcomes. The value of being sensitive to this geometry has been demonstrated, among others, in ordinal regression and generative modelling. In this paper we describe three natural properties of probability divergences that reflect requirements from machine learning: sum invariance, scale sensitivity, and unbiased sample gradients. The Wasserstein…
Universitat Autònoma de Barcelona（巴塞罗那自治大学）；Universitat de Barcelona（巴塞罗那大学）
(Conditional) Generative Adversarial Networks (GANs) have found great success in recent years, due to their ability to approximate (conditional) distributions over extremely high dimensional spaces. However, they are highly unstable and computationally expensive to train, especially in the time series setting. Recently, it has been proposed the use of a key object in rough path theory, called the signature of a path, which is able to convert the min-max formulation given by the (conditional) GAN framework into a classical minimization problem. However, this method is extremely expensive in ter…
A common problem when forecasting rare events, such as recessions, is limited data availability. Recent advancements in deep learning and generative adversarial networks (GANs) make it possible to produce high-fidelity synthetic data in large quantities. This paper uses a model called DoppelGANger, a GAN tailored to producing synthetic time series data, to generate synthetic Treasury yield time series and associated recession indicators. It is then shown that short-range forecasting performance for Treasury yields is improved for models trained on synthetic data relative to models trained only…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Cambridge（剑桥大学）
Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax rates of estimation have been established in recent years, many existing robust estimators with provably optimal convergence rates are also computationally intractable. In this paper, we study several estimation problems under a Wasserstein contamination model and present computationally tractable estimators motivated by generative adversarial networks (GANs)…
University of Iowa（爱荷华大学）；The Hong Kong University of Science and Technology（香港科技大学）；Wuhan University（武汉大学）
We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimation error under the Dudley distance between the latent joint distribution and the data joint distribution with appropriately specified architecture of the neural networks used in the model. To the best of our knowledge, this is the first theoretical guarantee for the bidirectional GAN learning approach. An appealing feature of our results is that they do not assume the reference and the data distributions to have the same dimensions or these distributions to have bounded support. These assumptions are commonly assumed in th…
