Differentiable Particle Filtering via Entropy-Regularized Optimal Transport
Adrien Corenflos, James Thornton, George Deligiannidis, Arnaud Doucet
Abstract
Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.
BibTeX
@InProceedings{pmlr-v139-corenflos21a,
title = {Differentiable Particle Filtering via Entropy-Regularized Optimal Transport},
author = {Corenflos, Adrien and Thornton, James and Deligiannidis, George and Doucet, Arnaud},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {2100--2111},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/corenflos21a/corenflos21a.pdf},
url = {https://proceedings.mlr.press/v139/corenflos21a.html},
abstract = {Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.}
}