Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching

Cagatay Yildiz; Markus Heinonen; Jukka Intosalmi; Henrik Mannerström; Harri Lähdesmäki

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arXiv · 1807.05748

Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching

Cagatay Yildiz·Markus Heinonen·Jukka Intosalmi·Henrik Mannerström·Harri Lähdesmäki

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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.

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Cagatay Yildiz, Markus Heinonen, Jukka Intosalmi, Henrik Mannerström, Harri Lähdesmäki. 2018-07-16. Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching. https://arxiv.org/abs/1807.05748

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