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

TL;DR

This paper introduces a new probabilistic approach for estimating drift and diffusion in stochastic differential equations using adversarial and MMD techniques, avoiding traditional discretization methods and improving accuracy and robustness.

Contribution

It presents a novel method combining adversarial and moment matching inference for SDE parameter estimation, outperforming classical discretization-based methods.

Findings

Significant improvements in parameter accuracy and robustness.

Outperforms extended Kalman filtering and Gaussian process methods.

Validated on four benchmark systems.

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.