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.

本文提出了一种新的时间序列生成器 —— 指向连锁 GAN（DC-GANs），该生成器可以生成与邻域过程具有相同分布的新时间序列，并且可以在生成多模态时间序列方面显着优于现有最佳方法。