Approximate Gaussian process inference for the drift function in stochastic differential equations

Part of Advances in Neural Information Processing Systems 26 (NIPS 2013)

Authors

Andreas Ruttor, Philipp Batz, Manfred Opper

Abstract

We introduce a nonparametric approach for estimating drift functions in systems of stochastic differential equations from incomplete observations of the state vector. Using a Gaussian process prior over the drift as a function of the state vector, we develop an approximate EM algorithm to deal with the unobserved, latent dynamics between observations. The posterior over states is approximated by a piecewise linearized process and the MAP estimation of the drift is facilitated by a sparse Gaussian process regression.