Methods and Uses of Graph Demoralization

Mary McGlohonSIGBOVIK

April 1, 2007

Motivation

• Moralization is an important tool in probabilistic graphical models

• The method of demoralization has not been properly addressed in research. Oh noes!

Demotivation

Outline for talk

Preliminaries: PGMs

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

Rain Temperature

PlayTennis

EnjoySport

Usual graph terms apply (parents, children, ancestors, descendents, cycles...)

Preliminaries: PGMs

• Each node has its very own conditional probability table.

Rain Temperature

PlayTennis

EnjoySport

T F

.8 .2

Hi Lo

.6 .4

Rain Temp PT=T PT=F

T Hi .2 .8

T Lo .3 .7

F Hi .4 .6

F Lo .1 .9PT ES=T ES=F

T .8 .2

F 0 1

Graph Moralization

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

X1 X2

X4X3

X5 X6

X7

Unmarried parents = immorality

We’re living in sin!

Graph Moralization

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

X1 X2

X4X3

X5 X6

X7

Unmarried parents = immorality

We’re living in sin!

Graph Moralization

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

X1 X2

X4X3

X5 X6

X7

Marry the parents = moralize

Saved by the power of Jesus!

Graph Moralization

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

X1 X2

X4X3

X5 X6

X7

Marry the parents = moralizeThen un-direct edges.

Disclaimer: The moral judgments represented by this preliminary section do not necessarily represent those of the author or the NSF.

Graph Demoralization

• 3 methods for demoralizing

X1 X2

X4X3

X5 X6

X7

Isolation

• Based on social group theory

X1 X2

X4X3

Isolation

X1 X2

X4X3

X5 X6

X7

Choose node(s) to isolate,Remove all edges to/from nodes.

Isolation

X1 X2

X4X3

X5 X6

X7

1 graph 5 separate graphs!Probability distribution is totally screwed!

Misdirection

• Also based on social group theory

X1 X2

X4X3

X5 X6

X7

Misdirection

X1 X2

X4X3

X5 X6

X7

Remove edge, direct it off the page.

Misdirection

X1 X2

X4X3

X5 X6

X7

Remove edge, direct it off the page.

Confuses probability distribution! Very demoralizing!

Disbelief Propagation

X1 X2

X4X3

X5 X6

X7

Condition disbelief on a node,Propagate disbelief through graph.

Disbelief Propagation

X1 X2

X4X3

X5 X6

X7

Awww.....

Applications

• Sating sadistic susceptibility of statisticians

More important than you’d think!

Statisticians are mean!

• The word “statistics” is nearly impossible to pronounce while drunk.

• But, stat homework is only tolerable in such an inebriated state.

E(statisticians)

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.

Conclusions

• Three methods for graph demoralization– Isolation– Misdirection– Disbelief Propagation

• Useful because statisticians like demoralizing things.

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. Metron’s Bayesian Houses. In Machine learning office conversations, 2007.

[4] D. Koller and N. Friedman. Probabilistic Graphical Models (DRAFT). Palo Alto, CA, 2007.

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.

Questions?