@inproceedings{
baker2024conditioning,
title={Conditioning non-linear and infinite-dimensional diffusion processes},
author={Elizabeth Louise Baker and Gefan Yang and Michael Lind Severinsen and Christy Anna Hipsley and Stefan Sommer},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=FV4an2OuFM}
}
Generative diffusion models and many stochastic models in science and engineering naturally live in infinite dimensions before discretisation. To incorporate observed data for statistical and learning tasks, one needs to condition on observations. While recent work has treated conditioning linear processes in infinite dimensions, conditioning non-linear processes in infinite dimensions has not been explored. This paper conditions function valued stochastic processes without prior discretisation. To do so, we use an infinite-dimensional version of Girsanov's theorem to condition a function-valued stochastic process, leading to a stochastic differential equation (SDE) for the conditioned process involving the score. We apply this technique to do time series analysis for shapes of organisms in evolutionary biology, where we discretise via the Fourier basis and then learn the coefficients of the score function with score matching methods.
Conditioning non-linear and infinite-dimensional diffusion processes
Elizabeth Louise Baker Gefan Yang Michael Lind Severinsen Christy Anna Hipsley Stefan Sommer