Consistent and Efficient Reconstruction of Latent Tree Models Myung Jin Choi Joint work with Vincent Tan, Anima Anandkumar, and Alan S. Willsky Laboratory for Information and Decision Systems Massachusetts Institute of Technology September 29, 2010 Stochastic Systems Group
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Consistent and Efficient Reconstruction of Latent Tree Models
Stochastic Systems Group. Consistent and Efficient Reconstruction of Latent Tree Models. Myung Jin Choi Joint work with Vincent Tan, Anima Anandkumar, and Alan S. Willsky Laboratory for Information and Decision Systems Massachusetts Institute of Technology September 29, 2010. - PowerPoint PPT Presentation
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Consistent and Efficient Reconstructionof Latent Tree Models
Myung Jin Choi
Joint work with Vincent Tan, Anima Anandkumar, and Alan S. Willsky
Laboratory for Information and Decision Systems Massachusetts Institute of Technology
September 29, 2010
Stochastic Systems Group
Latent Tree Graphical Models
Dell
CVS Disney
Microsoft
Apple
Latent Tree Graphical Models
Dell
CVS Disney
Microsoft
Apple
Computer
Computer Equipment
Market
Outline
– Reconstruction of a latent tree
– Algorithm 1: Recursive Grouping
– Algorithm 2: CLGrouping
– Experimental results
Reconstruction of a Latent Tree
Reconstruct a latent tree using samples of the observed nodes.
• Gaussian model:
each node – a scalar
Gaussian variable
• Discrete model:
each node – a discrete
variable with K states
Minimal Latent Trees (Pearl, 1988)
Conditions for Minimal Latent Trees• Each hidden node should have at least three neighbors.• Any two variables are neither perfectly dependent nor