AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs

By Gabriele Abbati, Philippe Wenk, Stefan Bauer, Michael A. Osborne, Andreas Krause, Bernhard Schölkopf. 2019

15 citations recorded by the source corpus.

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.