Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching
This addresses the problem of modeling complex dynamic systems for researchers in fields like finance or biology, though it appears incremental as it builds on existing SDE learning approaches.
The paper tackles learning stochastic differential equations (SDEs) by introducing a method that simulates path distributions to match observations with non-uniform time increments and sparseness, achieving robust and efficient learning without gradient matching.
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.