Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

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This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.



Original languageEnglish
Article number012148
Number of pages15
JournalPhysical Review E
Issue number1
StatePublished - 30 Jan 2015

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© American Physical Society Funding: European FP7 grant under the GeoViQua project (Environment; 265178), and under the CompLACS grant (ICT; 270327)

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