Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching

TL;DR

This paper presents a new method for learning stochastic differential equations using Gaussian processes that directly optimizes path distributions, improving robustness and efficiency over traditional gradient matching techniques.

Contribution

It introduces a novel paradigm for learning SDEs that does not rely on gradient matching, enabling robust learning from sparse and irregular data.

Findings

Effective learning of SDEs from sparse data

Robust and efficient parameter estimation

Improved simulation accuracy of path distributions

Abstract

We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time increments and arbitrary sparseness, which is in contrast with gradient matching that does not optimize simulated responses. We formulate sensitivity equations for learning and demonstrate that our general stochastic distribution optimisation leads to robust and efficient learning of SDE systems.