Variational Bayesian inference for partially observed stochastic dynamical systems

In this paper the variational Bayesian approximation for partially observed continuous time stochastic processes is studied. We derive an EM-like algorithm and describe its implementation. The variational Expectation step is explicitly solved using the method of conditional moment generating functions and stochastic partial differential equations. The numerical experiments demonstrate that the variational Bayesian estimate is more robust than the EM algorithm.

[1]  Charalambos D. Charalambous,et al.  Maximum likelihood parameter estimation from incomplete data via the sensitivity equations: the continuous-time case , 2000, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[2]  Robert J. Elliott,et al.  Classes of Nonlinear Partially Observable Stochastic Optimal Control Problems with Explicit Optimal Control Laws , 1998 .

[3]  R. Elliott,et al.  Conditional moment generating functions for integrals and stochastic integrals , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[4]  Robert J. Elliott,et al.  Exact Finite-Dimensional Filters for Maximum Likelihood Parameter Estimation of Continuous-time Linear Gaussian Systems , 1997 .

[5]  R. Elliott,et al.  Certain nonlinear partially observable stochastic optimal control problems with explicit control laws equivalent to LEQG/LQG problems , 1997, IEEE Trans. Autom. Control..

[6]  Michael I. Jordan,et al.  Mean Field Theory for Sigmoid Belief Networks , 1996, J. Artif. Intell. Res..

[7]  Geoffrey E. Hinton,et al.  Keeping the neural networks simple by minimizing the description length of the weights , 1993, COLT '93.

[8]  F. Gland,et al.  MLE for partially observed diffusions: direct maximization vs. the em algorithm , 1989 .

[9]  Etienne Pardoux,et al.  A conditionally almost Linear filtering problem with non-Gaussian initial condition , 1988 .

[10]  V. Benes.  Exact finite-dimensional filters for certain diffusions with nonlinear drift , 1981 .

[11]  J. Shawe-Taylor,et al.  Variational Inference in Stochastic Dynamic Environmental Models , 2005 .

[12]  D. Titterington,et al.  Approximate Bayesian inference for simple mixtures , 2000 .

[13]  Michael I. Jordan,et al.  Advances in Neural Information Processing Systems 30 , 1995 .