Approximate Bayes learning of stochastic differential equations Article Swipe

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Stochastic differential equation Piecewise Mathematics Applied mathematics Gaussian process Maximum a posteriori estimation Gaussian Ornstein–Uhlenbeck process Mathematical optimization Nonparametric regression Expectation–maximization algorithm Stochastic approximation Diffusion process Nonparametric statistics Stochastic process Computer science Mathematical analysis Statistics Maximum likelihood Physics Innovation diffusion Quantum mechanics Key (lock) Knowledge management Computer security

Philipp Batz , Andreas Ruttor , Manfred Opper ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.1103/physreve.98.022109 · OA: W2590864591

We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions, and estimates are calculated directly from dense data sets using Gaussian process regression. We develop an approximate expectation maximization algorithm to deal with the unobserved, latent dynamics between sparse observations. The posterior over states is approximated by a piecewise linearized process of the Ornstein-Uhlenbeck type and the maximum a posteriori estimation of the drift is facilitated by a sparse Gaussian process approximation.

Approximate Bayes learning of stochastic differential equations Article Swipe

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