1999 AnIntroductiontoVariationalMeth

• (Jordan et al., 1999) ⇒ Michael I. Jordan, Zoubin Ghahramani, Tommi S. Jaakkola, and Lawrence K. Saul. (1999). “An Introduction to Variational Methods for Graphical Models.” In: Machine Learning Journal, 37(2). doi:10.1023/A:1007665907178

Subject Headings:

Notes

• Tech report: http://stat-www.berkeley.edu/tech-reports/508.pdf

Cited By

• ~1186 http://scholar.google.com/scholar?q=%22An+Introduction+to+Variational+Methods+for+Graphical+Models%22+1999
• http://dl.acm.org/citation.cfm?id=339248.339252&preflayout=flat#citedby

Quotes

Author Keywords

• Bayesian networks; Boltzmann machines; approximate inference; belief networks; graphical models; hidden Markov models; mean field methods; neural networks; probabilistic inference; variational methods

Abstract

This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields). We present a number of examples of graphical models, including the QMR-DT database, the sigmoid belief network, the Boltzmann machine, and several variants of hidden Markov models, in which it is infeasible to run exact inference algorithms. We then introduce variational methods, which exploit laws of large numbers to transform the original graphical model into a simplified graphical model in which inference is efficient. Inference in the simpified model provides bounds on probabilities of interest in the original model. We describe a general framework for generating variational transformations based on convex duality. Finally we return to the examples and demonstrate how variational algorithms can be formulated in each case.

References

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
1999 AnIntroductiontoVariationalMeth	Zoubin Ghahramani Tommi S. Jaakkola Lawrence K. Saul			An Introduction to Variational Methods for Graphical Models				10.1023/A:1007665907178