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Expectation propagation for continuous time stochastic processes
Citation key CsSchOpSa16
Author Botond Cseke and David Schnoerr and Manfred Opper and Guido Sanguinetti
Pages 494002
Year 2016
DOI http://dx.doi.org/10.1088/1751-8113/49/49/494002
Journal Journal of Physics A: Mathematical and Theoretical
Volume 49
Number 49
Publisher IOPscience
Abstract We consider the inverse problem of reconstructing the posterior measure over the trajectories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference, giving rise to an expectation propagation type algorithm. For non-linear diffusion processes, this is achieved by leveraging moment closure approximations. We then show how the approximation can be extended to a wide class of discrete-state Markov jump processes by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems.
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