Real-world data can be multimodal distributed, e.g., data describing the opinion divergence in a community, the interspike interval distribution of neurons, and the oscillators natural frequencies. Generating multimodal distributed real-world data has become a challenge to existing generative adversarial networks (GANs). For example, neural stochastic differential equations (Neural SDEs), treated as infinite-dimensional GANs, have demonstrated successful performance mainly in generating unimodal time series data. In this paper, we propose a novel time series generator, named directed chain GANs (DC-GANs), which inserts a time series dataset (called a neighborhood process of the directed chain or input) into the drift and diffusion coefficients of the directed chain SDEs with distributional constraints. DC-GANs can generate new time series of the same distribution as the neighborhood process, and the neighborhood process will provide the key step in learning and generating multimodal distributed time series. The proposed DC-GANs are examined on four datasets, including two stochastic models from social sciences and computational neuroscience, and two real-world datasets on stock prices and energy consumption. To our best knowledge, DC-GANs are the first work that can generate multimodal time series data and consistently outperforms state-of-the-art benchmarks with respect to measures of distribution, data similarity, and predictive ability.

翻译：真实世界的数据可呈现多模态分布，例如描述社区观点分歧的数据、神经元峰电位间隔分布以及振子自然频率等。生成多模态分布的真实数据已成为现有生成对抗网络（GANs）面临的挑战。例如，被视为无限维生成对抗网络的神经随机微分方程（Neural SDEs）主要在单峰时间序列数据生成方面取得了成功。本文提出一种新型时间序列生成器——定向链生成对抗网络（DC-GANs），该方法将时间序列数据集（称为定向链邻域过程或输入）引入带有分布约束的定向链随机微分方程的漂移系数与扩散系数中。DC-GANs能够生成与邻域过程同分布的新时间序列，而邻域过程将为学习与生成多模态分布时间序列提供关键步骤。我们在四个数据集上验证了所提出的DC-GANs，包括来自社会科学与计算神经科学的两个随机模型，以及关于股票价格与能源消耗的两个真实世界数据集。据我们所知，DC-GANs是首个能够生成多模态时间序列数据的方法，并且在分布度量、数据相似性与预测能力方面持续优于当前最先进的基准方法。