### Abstract

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 language | English |
---|---|

Article number | 012148 |

Number of pages | 15 |

Journal | Physical Review E |

Volume | 91 |

Issue number | 1 |

DOIs | |

Publication status | Published - 30 Jan 2015 |

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### Bibliographical note

© American Physical SocietyFunding: European FP7 grant under the GeoViQua project (Environment; 265178),

and under the CompLACS grant (ICT; 270327)

### Cite this

*Physical Review E*,

*91*(1), [012148]. https://doi.org/10.1103/PhysRevE.91.012148

}

*Physical Review E*, vol. 91, no. 1, 012148. https://doi.org/10.1103/PhysRevE.91.012148

**Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations.** / Vrettas, Michail D.; Opper, Manfred; Cornford, Dan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

AU - Vrettas, Michail D.

AU - Opper, Manfred

AU - Cornford, Dan

N1 - © American Physical Society Funding: European FP7 grant under the GeoViQua project (Environment; 265178), and under the CompLACS grant (ICT; 270327)

PY - 2015/1/30

Y1 - 2015/1/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84921939737&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.91.012148

DO - 10.1103/PhysRevE.91.012148

M3 - Article

AN - SCOPUS:84921939737

VL - 91

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - 012148

ER -