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

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

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Andreas Ruttor, Philipp Batz, Manfred Opper


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.