Methods and Uses of Graph Demoralization

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Methods and Uses of Graph Demoralization

• Mary McGlohon
• SIGBOVIK
• April 1, 2007

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Motivation

• Moralization is an important tool in
  probabilistic graphical models
• The method of demoralization has not been
  properly addressed in research. Oh noes!

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Demotivation
4
Outline for talk
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Preliminaries PGMs

• Probabilistic models can be represented by
  graphs.
• Nodes Random Variables
• Edges Dependencies between RVs

Rain
Temperature
Usual graph terms apply (parents, children,
ancestors, descendents, cycles...)
PlayTennis
EnjoySport
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Preliminaries PGMs

• Each node has its very own conditional
  probability table.

Hi Lo
.6 .4
T F
.8 .2
Rain
Temperature
Rain Temp PTT PTF
T Hi .2 .8
T Lo .3 .7
F Hi .4 .6
F Lo .1 .9
PlayTennis
PT EST ESF
T .8 .2
F 0 1
EnjoySport
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Graph Moralization

• To convert from directed to undirected graphical
  model, it is necessary to moralize the graph.

Were living in sin!
X1
X2
Unmarried parents immorality
X4
X3
X5
X6
X7
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Graph Moralization

• To convert from directed to undirected graphical
  model, it is necessary to moralize the graph.

Were living in sin!
X1
X2
Unmarried parents immorality
X4
X3
X5
X6
X7
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Graph Moralization

• To convert from directed to undirected graphical
  model, it is necessary to moralize the graph.

Saved by the power of Jesus!
X1
X2
Marry the parents moralize
X4
X3
X5
X6
X7
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Graph Moralization

• To convert from directed to undirected graphical
  model, it is necessary to moralize the graph.

X1
X2
Marry the parents moralize Then un-direct edges.
X4
X3
X5
X6
X7
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Graph Demoralization

• 3 methods for demoralizing

X1
X2
X4
X3
X5
X6
X7
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Isolation

• Based on social group theory

X1
X2
X4
X3
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Isolation
Choose node(s) to isolate, Remove all edges
to/from nodes.
X1
X2
X4
X3
X5
X6
X7
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Isolation
1 graph ? 5 separate graphs! Probability
distribution is totally screwed!
X1
X2
X4
X3
X5
X6
X7
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Misdirection

• Also based on social group theory

X1
X2
X4
X3
X5
X6
X7
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Misdirection
Remove edge, direct it off the page.
X1
X2
X4
X3
X5
X6
X7
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Misdirection
Remove edge, direct it off the page.
X1
X2
Confuses probability distribution! Very
demoralizing!
X4
X3
X5
X6
X7
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Disbelief Propagation
?
Condition disbelief on a node, Propagate
disbelief through graph.
X1
X2
?
X4
X3
?
?
X5
X6
?
X7
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Disbelief Propagation
?
Awww.....
X1
X2
?
X4
X3
?
?
X5
X6
?
X7
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Applications

• Sating sadistic susceptibility of statisticians

More important than youd think!
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Statisticians are mean!
E(statisticians)

• The word statistics is nearly impossible to
  pronounce while drunk.
• But, stat homework is only tolerable in such an
  inebriated state.

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Statisticians are mean!

• Turf war between frequentists and Bayesians
• ? Rap battle between
• The Unbiased M.L.E. and Emcee MC

This is a Bayesian House.
I can say with 95 confidence that your ass will
contain my foot.
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Conclusions

• Three methods for graph demoralization
• Isolation
• Misdirection
• Disbelief Propagation
• Useful because statisticians like demoralizing
  things.

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References

• 1 A. Arnold. Chronicles of the
  Bayesian-Frequentist Wars. somewhere in Europe
  with .75 probability, 1999.
• 2 C. Bishop. Pattern Recognition and Machine
  Learning 23 cents cheaper per page than Tom
  Mitchell's book. Springer Texts, New York, 2006.
• 3 K. El-Arini. Metrons Bayesian Houses. In
  Machine learning office conversations, 2007.
• 4 D. Koller and N. Friedman. Probabilistic
  Graphical Models (DRAFT). Palo Alto, CA, 2007.

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References

• 4 T. Mitchell. Machine Learning. McGraw-Hill,
  New York, 1997.
• 5 E. Stiehl. Misdirected and isolating groups
  and their subsequent demoralization.
  Conversations with resident business grad student
  at Machine Learning Department holiday parties,
  2006.
• 6 L.Wasserman. All of Statistics. Pink Book
  Publishing, New York.
• 7 L. Wasserman and J. Lafferty. All of
  Statistical Ma-chine Learning. (DRAFT) Pink Book
  Publishing, New York.

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Questions?