Tuesday, February 13th @ 11:00-12:30 PM, Zoom
Real-world financial data can be multimodal distributed, and 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, are only capable of generating unimodal time series data. In this talk, we present 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. Signature from rough path theory will be used to construct the discriminator. Numerical experiments on financial data are presented and show a consistent outperformance over state-of-the-art benchmarks with respect to measures of distribution, data similarity, and predictive ability. If time permits, I will also talk about using Signature to solve mean-field games with common noise.