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Title: Nonparametric learning of stochastic differential equations Authors:  Andreas Ruttor - TU Berlin (Germany) [presenting]
Philipp Batz - TU Berlin (Germany)
Manfred Opper - TU Berlin (Germany)
Abstract: Differential equations are suitable models for many real-world systems, but prior knowledge about their structure may be limited or missing. While parametric drift and diffusion functions could be chosen by model selection, it is often difficult to specify a good set of candidates in order to avoid model mismatch. A better approach is to use nonparametric Bayesian inference for estimating complete functions. That way both drift and diffusion functions for a system of stochastic differential equations are learned 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. In case of sparse observations the latent dynamics between data points is estimated by an approximate expectation maximisation algorithm. Here 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.