A Comparison of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems

被引：0
作者：
Yuan Shen
Cedric Archambeau
Dan Cornford
Manfred Opper
John Shawe-Taylor
Remi Barillec
机构：
[1] Aston University,Neural Computing Research Group
[2] University College London,Department of Computer Science
[3] Technical University Berlin,Artificial Intelligence Group
来源：
Journal of Signal Processing Systems | 2010年 / 61卷
关键词：
Data assimilation; Signal processing; Nonlinear smoothing; Variational approximation; Bayesian computation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother.
引用
收藏
页码：51 / 59
页数：8
相关论文
共 38 条
  • [1] Kushner H. J.(1967)Dynamical equations for optimal filter Journal of Differential Equations 3 179-190
  • [2] Stratonovich R. L.(1960)Conditional markov processes Theory of Probability and Its Applications 5 156-178
  • [3] Pardoux E.(1982)Équations du filtrage non linéaire de la prédiction et du lissage Stochastics 6 193-231
  • [4] Kalman R. E.(1961)New results in linear filtering and prediction theory Journal of Basic Engineering 83D 95-108
  • [5] Bucy R. S.(2007)Gaussian process approximations of stochastic differential equations Journal of Machine Learning Research Workshop and Conference Proceedings 1 1-16
  • [6] Archambeau C.(2003)An introduction to MCMC for machine learning Machine Learning 50 5-43
  • [7] Cornford D.(2005)Accelerated Monte Carlo for optimal estimation of time series Journal of Statistical Physics 119 1331-1345
  • [8] Opper M.(1992)Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model Journal of Geophysical Research 97 17905-17924
  • [9] Shawe-Tayler J.(1994)Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics Journal of Geophysical Research 99 10143-10162
  • [10] Andrieu C.(1987)Non-Gaussian state space modelling of non-stationary time series Journal of the American Statistical Association 82 503-514
1234