Motivation
• Moralization is an important tool in probabilistic graphical models
• The method of demoralization has not been properly addressed in research. Oh noes!
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.
Isolation
X1 X2
X4X3
X5 X6
X7
1 graph 5 separate graphs!Probability distribution is totally screwed!
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.
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.