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 commonly used benchmark systems, we demonstrate the performance of our algorithms compared to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.

@inproceedings{wenk2019Ares,
	author = {Abbati, Gabriele and Wenk, Philippe and Bauer, Stefan and Osborne, Michael A and Krause, Andreas and Sch\"olkopf, Bernhard},
	booktitle = {Proc. International Conference on Machine Learning (ICML)},
	journal = {arXiv preprint arXiv:1902.08480},
	month = {June},
	title = {AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs},
	year = {2019}}