Non-adversarial training of Neural SDEs with signature kernel scores
Author(s)
Issa, Zacharia
Horvath, Blanka
Lemercier, Maud
Salvi, Cristopher
Type
Conference Paper
Abstract
Neural SDEs are continuous-time generative models for sequential data. State-of-the-art performance for irregular time series generation has been previously obtained by training these models adversarially as GANs. However, as typical for GAN architectures, training is notoriously unstable, often suffers from mode collapse, and requires specialised techniques such as weight clipping and gradient penalty to mitigate these issues. In this paper, we introduce a novel class of scoring rules on pathspace based on signature kernels and use them as objective for training Neural SDEs non-adversarially. By showing strict properness of such kernel scores and consistency of the corresponding estimators, we provide existence and uniqueness guarantees for the minimiser. With this formulation, evaluating the generator-discriminator pair amounts to solving a system of linear path-dependent PDEs which allows for memory-efficient adjoint-based backpropagation. Moreover, because the proposed kernel scores are well-defined for paths with values in infinite dimensional spaces of functions, our framework can be easily extended to generate spatiotemporal data. Our procedure significantly outperforms alternative ways of training Neural SDEs on a variety of tasks including the simulation of rough volatility models, the conditional probabilistic forecasts of real-world forex pairs where the conditioning variable is an observed past trajectory, and the mesh-free generation of limit order book dynamics.
Date Issued
2023-12-10
Date Acceptance
2023-05-01
Citation
Advances in neural information processing systems, 2023, 36, pp.11102-11126
ISSN
1049-5258
Publisher
Curran Associates, Inc.
Start Page
11102
End Page
11126
Journal / Book Title
Advances in neural information processing systems
Volume
36
Copyright Statement
© 2023 The Author(s) and NeurIPS.
Source
Advances in neural information processing systems (NeurIPS)
Publication Status
Published
Start Date
2023-12-10
Finish Date
2023-12-16
Coverage Spatial
New Orleans, LA, USA