Download - Methods and Uses of Graph Demoralization

Transcript
Page 1: Methods and Uses of Graph Demoralization

Methods and Uses of Graph Demoralization

Mary McGlohonSIGBOVIK

April 1, 2007

Page 2: Methods and Uses of Graph Demoralization

Motivation

• Moralization is an important tool in probabilistic graphical models

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

Page 3: Methods and Uses of Graph Demoralization

Demotivation

Page 4: Methods and Uses of Graph Demoralization

Outline for talk

Page 5: Methods and Uses of Graph Demoralization

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...)

Page 6: Methods and Uses of Graph Demoralization

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

Page 7: Methods and Uses of Graph Demoralization

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!

Page 8: Methods and Uses of Graph Demoralization

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!

Page 9: Methods and Uses of Graph Demoralization

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!

Page 10: Methods and Uses of Graph Demoralization

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.

Page 11: Methods and Uses of Graph Demoralization

Graph Demoralization

• 3 methods for demoralizing

X1 X2

X4X3

X5 X6

X7

Page 12: Methods and Uses of Graph Demoralization

Isolation

• Based on social group theory

X1 X2

X4X3

Page 13: Methods and Uses of Graph Demoralization

Isolation

X1 X2

X4X3

X5 X6

X7

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

Page 14: Methods and Uses of Graph Demoralization

Isolation

X1 X2

X4X3

X5 X6

X7

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

Page 15: Methods and Uses of Graph Demoralization

Misdirection

• Also based on social group theory

X1 X2

X4X3

X5 X6

X7

Page 16: Methods and Uses of Graph Demoralization

Misdirection

X1 X2

X4X3

X5 X6

X7

Remove edge, direct it off the page.

Page 17: Methods and Uses of Graph Demoralization

Misdirection

X1 X2

X4X3

X5 X6

X7

Remove edge, direct it off the page.

Confuses probability distribution! Very demoralizing!

Page 18: Methods and Uses of Graph Demoralization

Disbelief Propagation

X1 X2

X4X3

X5 X6

X7

Condition disbelief on a node,Propagate disbelief through graph.

Page 19: Methods and Uses of Graph Demoralization

Disbelief Propagation

X1 X2

X4X3

X5 X6

X7

Awww.....

Page 20: Methods and Uses of Graph Demoralization

Applications

• Sating sadistic susceptibility of statisticians

More important than you’d think!

Page 21: Methods and Uses of Graph Demoralization

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)

Page 22: Methods and Uses of Graph Demoralization

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.

Page 23: Methods and Uses of Graph Demoralization

Conclusions

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

• Useful because statisticians like demoralizing things.

Page 24: Methods and Uses of Graph Demoralization

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.

Page 25: Methods and Uses of Graph Demoralization

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.

Page 26: Methods and Uses of Graph Demoralization

Questions?