Junction Tree Algorithm Examples October 13, 2016 Junction Tree - - PowerPoint PPT Presentation

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Junction Tree Algorithm Examples October 13, 2016 Junction Tree - - PowerPoint PPT Presentation

Junction Tree Algorithm Examples October 13, 2016 Junction Tree Algorithm Moralize (if starting from a directed graphical model) Triangulate (make it chordal) Construct a junction tree (maximum cardinality search) Define


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SLIDE 1

Junction Tree Algorithm Examples

October 13, 2016

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Junction Tree Algorithm

  • Moralize (if starting from a directed graphical

model)

  • Triangulate (make it chordal)
  • Construct a junction tree (maximum cardinality

search)

  • Define potentials on maximal cliques
  • Introduce evidence (if any)
  • Propagate probabilities
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SLIDE 3

CHILD Example from Spiegelhalter et al (1993) Statistical Science

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SLIDE 4

Conditional Probability Tables

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Visualization of Updated Beliefs on Every Node

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SLIDE 6

Visualization of Updated Beliefs on Every Node

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SLIDE 7

Moralize

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Triangulation and Maximum Cardinality Search

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SLIDE 9

Construct Junction Tree and Define Potentials on Maximal Cliques

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SLIDE 10

Introduce Evidence and Propagate Probabilities

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SLIDE 11

Comments:

  • 1. Read Spiegelhalter, David J.; Dawid, A. Philip; Lauritzen, Steffen L.; Cowell, Robert
  • G. Bayesian Analysis in Expert Systems. Statist. Sci. 8 (1993), no. 3, 219--247. doi:

10.1214/ss/1177010888. http://projecteuclid.org/euclid.ss/1177010888.

  • 2. Convince yourself the numbers in Figure 13 are correct.
  • 3. We will proceed to approximate inference.
  • 4. Enjoy your Fall break!
  • 5. Fill out the midterm survey: https://goo.gl/forms/AMfJ1t1d0gQbgQXI3
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SLIDE 13