# Variational Inference for State Dependent Diffusion Processes

Author(s):T. Sutter |
Conference/Journal:Master Thesis, FS12 (10083) |

Abstract:Diffusion processes modeled by stochastic differential equations (SDEs) are widely used in several disciplines varying form mathematical finance to systems biology. Oftentimes, the state of the system is not directly observed and inference of the state trajectories has to be achieved based on noisy partial observations. Estimation of the hidden states given the data requires evaluation of appropriate conditional densities (posterior densities) which are often solutions to suitable, both analytically and numerically complex, partial differential equations (PDEs). In this report, we present a new approach to the inference problem for SDEs. The main idea is to approximate the posterior probability distribution by a distribution from the exponential family (e.g. a Gaussian). The parameters of the approximating distribution (that are functions of time) are obtained by minimizing the Kullback- Leibler divergence between the posterior process and the approximating SDE. We show that this (infinite-dimensional) optimization problem, and therefore the inference problem for SDEs, can be recast as a standard optimal control problem. Hence, instead of dealing with an infinite-dimensional PDE, we just have to solve a system of ordinary differential equations. | Year:2012 |

Type of Publication:(12)Diploma/Master Thesis | |

Supervisor:H. Koeppl | |

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% Autogenerated BibTeX entry @PhdThesis { Xxx:2012:IFA_4191 } | |

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