AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs
This work addresses parameter estimation in SDEs, a foundational modeling class in many disciplines, by introducing a novel probabilistic approach that avoids discretization schemes.
The authors tackled the problem of estimating drift and diffusion parameters in stochastic differential equations from noisy observations, achieving significant improvements in parameter accuracy and robustness compared to state-of-the-art methods like extended Kalman filtering and Gaussian processes.
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.