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

We introduce a nonparametric approach for estimating drift functions in systems of stochastic differential equations from sparse observat ions 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 unobser ved, latent dynamics between observations. The posterior over states is appr oximated by a piecewise linearized process of the Ornstein-Uhlenbeck type and the M AP estimation of the drift is facilitated by a sparse Gaussian process regressio n.