Variational Inference for continuous Sigmoidal Bayesian Networks

Brendan J. Frey
Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics, PMLR R1:211-222, 1997.

Abstract

Latent random variables can be useful for modelling covariance relationships between observed variables. The choice of whether specific latent variables ought to be continuous or discrete is often an arbitrary one. In a previous paper, I presented a "unit" that could adapt to be continuous or binary, as appropriate for the current problem, and showed how a Markov chain Monte Carlo method could be used for inference and parameter estimation in Bayesian networks of these units. In this paper, I develop a variational inference technique in the hope that it will prove to be more computationally efficient than Monte Carlo methods. After presenting promising \emph{inference} results on a toy problem, I discuss why the variational technique does not work well for \emph{parameter estimation} as compared to Monte Carlo.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR1-frey97a, title = {Variational Inference for continuous Sigmoidal Bayesian Networks}, author = {Frey, Brendan J.}, booktitle = {Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics}, pages = {211--222}, year = {1997}, editor = {Madigan, David and Smyth, Padhraic}, volume = {R1}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/r1/frey97a/frey97a.pdf}, url = {https://proceedings.mlr.press/r1/frey97a.html}, abstract = {Latent random variables can be useful for modelling covariance relationships between observed variables. The choice of whether specific latent variables ought to be continuous or discrete is often an arbitrary one. In a previous paper, I presented a "unit" that could adapt to be continuous or binary, as appropriate for the current problem, and showed how a Markov chain Monte Carlo method could be used for inference and parameter estimation in Bayesian networks of these units. In this paper, I develop a variational inference technique in the hope that it will prove to be more computationally efficient than Monte Carlo methods. After presenting promising \emph{inference} results on a toy problem, I discuss why the variational technique does not work well for \emph{parameter estimation} as compared to Monte Carlo.}, note = {Reissued by PMLR on 30 March 2021.} }
Endnote
%0 Conference Paper %T Variational Inference for continuous Sigmoidal Bayesian Networks %A Brendan J. Frey %B Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1997 %E David Madigan %E Padhraic Smyth %F pmlr-vR1-frey97a %I PMLR %P 211--222 %U https://proceedings.mlr.press/r1/frey97a.html %V R1 %X Latent random variables can be useful for modelling covariance relationships between observed variables. The choice of whether specific latent variables ought to be continuous or discrete is often an arbitrary one. In a previous paper, I presented a "unit" that could adapt to be continuous or binary, as appropriate for the current problem, and showed how a Markov chain Monte Carlo method could be used for inference and parameter estimation in Bayesian networks of these units. In this paper, I develop a variational inference technique in the hope that it will prove to be more computationally efficient than Monte Carlo methods. After presenting promising \emph{inference} results on a toy problem, I discuss why the variational technique does not work well for \emph{parameter estimation} as compared to Monte Carlo. %Z Reissued by PMLR on 30 March 2021.
APA
Frey, B.J.. (1997). Variational Inference for continuous Sigmoidal Bayesian Networks. Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R1:211-222 Available from https://proceedings.mlr.press/r1/frey97a.html. Reissued by PMLR on 30 March 2021.

Related Material