Robust and Scalable SDE Learning: A Functional Perspective
Scott Alexander Cameron, Tyron Luke Cameron, Arnu Pretorius, Stephen J. Roberts
Abstract
Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and other flexible function approximators. Despite these advances, learning remains computationally expensive due to the sequential nature of SDE integrators. In this work, we propose an importance-sampling estimator for probabilities of observations of SDEs for the purposes of learning. Crucially, the approach we suggest does not rely on such integrators. The proposed method produces lower-variance gradient estimates compared to algorithms based on SDE integrators and has the added advantage of being embarrassingly parallelizable. This facilitates the effective use of large-scale parallel hardware for massive decreases in computation time.
BibTeX
@inproceedings{
cameron2022robust,
title={Robust and Scalable {SDE} Learning: A Functional Perspective},
author={Scott Alexander Cameron and Tyron Luke Cameron and Arnu Pretorius and Stephen J. Roberts},
booktitle={International Conference on Learning Representations},
year={2022},
url={https://openreview.net/forum?id=xZ6H7wydGl}
}