AReS and MaRS Adversarial and MMD-Minimizing Regression for SDEs

Gabriele Abbati, Philippe Wenk, Michael A. Osborne, Andreas Krause, Bernhard Schölkopf, Stefan Bauer
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:1-10, 2019.

Abstract

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-abbati19a, title = {{AR}e{S} and {M}a{RS} Adversarial and {MMD}-Minimizing Regression for {SDE}s}, author = {Abbati, Gabriele and Wenk, Philippe and Osborne, Michael A. and Krause, Andreas and Sch{\"o}lkopf, Bernhard and Bauer, Stefan}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {1--10}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/abbati19a/abbati19a.pdf}, url = {https://proceedings.mlr.press/v97/abbati19a.html}, abstract = {Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.} }
Endnote
%0 Conference Paper %T AReS and MaRS Adversarial and MMD-Minimizing Regression for SDEs %A Gabriele Abbati %A Philippe Wenk %A Michael A. Osborne %A Andreas Krause %A Bernhard Schölkopf %A Stefan Bauer %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-abbati19a %I PMLR %P 1--10 %U https://proceedings.mlr.press/v97/abbati19a.html %V 97 %X Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.
APA
Abbati, G., Wenk, P., Osborne, M.A., Krause, A., Schölkopf, B. & Bauer, S.. (2019). AReS and MaRS Adversarial and MMD-Minimizing Regression for SDEs. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:1-10 Available from https://proceedings.mlr.press/v97/abbati19a.html.

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