Lack of consistency of mean field and variational Bayes approximations for state space models

B. Wang; D.M. Titterington

doi:10.1007/s11063-004-2024-6

Lack of consistency of mean field and variational Bayes approximations for state space models

B. Wang, D.M. Titterington

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The consistency problem of both mean field and variational Bayes estimators in the context of linear state space models is investigated. We prove that the mean field approximation is asymptotically consistent when the variances of the noise variables in the system are sufficiently small, but neither the mean field estimator nor the variational Bayes estimator is always asymptotically consistent as the lsquosample sizersquo becomes large. The lsquogaprsquo between the estimators and the true values is roughly estimated.

Original language	English
Pages (from-to)	151-170
Number of pages	19
Journal	Neural Processing Letters
Volume	20
Issue number	3
DOIs	https://doi.org/10.1007/s11063-004-2024-6
Publication status	Published - Nov 2004

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10.1007/s11063-004-2024-6

http://dx.doi.org/10.1007/s11063-004-2024-6

Cite this

@article{ebd36c1583584c7a85724767eb09db37,

title = "Lack of consistency of mean field and variational Bayes approximations for state space models",

abstract = "The consistency problem of both mean field and variational Bayes estimators in the context of linear state space models is investigated. We prove that the mean field approximation is asymptotically consistent when the variances of the noise variables in the system are sufficiently small, but neither the mean field estimator nor the variational Bayes estimator is always asymptotically consistent as the lsquosample sizersquo becomes large. The lsquogaprsquo between the estimators and the true values is roughly estimated.",

author = "B. Wang and D.M. Titterington",

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doi = "10.1007/s11063-004-2024-6",

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AU - Titterington, D.M.

PY - 2004/11

Y1 - 2004/11

N2 - The consistency problem of both mean field and variational Bayes estimators in the context of linear state space models is investigated. We prove that the mean field approximation is asymptotically consistent when the variances of the noise variables in the system are sufficiently small, but neither the mean field estimator nor the variational Bayes estimator is always asymptotically consistent as the lsquosample sizersquo becomes large. The lsquogaprsquo between the estimators and the true values is roughly estimated.

AB - The consistency problem of both mean field and variational Bayes estimators in the context of linear state space models is investigated. We prove that the mean field approximation is asymptotically consistent when the variances of the noise variables in the system are sufficiently small, but neither the mean field estimator nor the variational Bayes estimator is always asymptotically consistent as the lsquosample sizersquo becomes large. The lsquogaprsquo between the estimators and the true values is roughly estimated.

U2 - 10.1007/s11063-004-2024-6

DO - 10.1007/s11063-004-2024-6

M3 - Article

SN - 1573-773X

VL - 20

SP - 151

EP - 170

JO - Neural Processing Letters

JF - Neural Processing Letters

IS - 3

ER -