Methods and Uses of Graph Demoralization

1. Methods and Uses of Graph Demoralization Mary McGlohon SIGBOVIK April 1, 2007

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

3. Demotivation

4. Outline for talk

5. 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

6. Preliminaries: PGMs • Each node has its very own conditional probability table. Rain Temperature PlayTennis EnjoySport

7. Graph Moralization • To convert from directed to undirected graphical model, it is necessary to moralize the graph. We’re living in sin! X1 X2 Unmarried parents = immorality X3 X4 X5 X6 X7

8. Graph Moralization • To convert from directed to undirected graphical model, it is necessary to moralize the graph. We’re living in sin! X1 X2 Unmarried parents = immorality X3 X4 X5 X6 X7

9. 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 X3 X4 X5 X6 X7

10. 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. Disclaimer: The moral judgments represented by this preliminary section do not necessarily represent those of the author or the NSF. X3 X4 X5 X6 X7

11. Graph Demoralization • 3 methods for demoralizing X1 X2 X3 X4 X5 X6 X7

12. Isolation • Based on social group theory X1 X2 X3 X4

13. Isolation Choose node(s) to isolate, Remove all edges to/from nodes. X1 X2 X3 X4 X5 X6 X7

14. Isolation 1 graph  5 separate graphs! Probability distribution is totally screwed! X1 X2 X3 X4 X5 X6 X7

15. Misdirection • Also based on social group theory X1 X2 X3 X4 X5 X6 X7

16. Misdirection Remove edge, direct it off the page. X1 X2 X3 X4 X5 X6 X7

17. Misdirection Remove edge, direct it off the page. X1 X2 Confuses probability distribution! Very demoralizing! X3 X4 X5 X6 X7

18. Disbelief Propagation  Condition disbelief on a node, Propagate disbelief through graph. X1 X2  X3 X4   X5 X6  X7

19. Disbelief Propagation  Awww..... X1 X2  X3 X4   X5 X6  X7

20. Applications • Sating sadistic susceptibility of statisticians More important than you’d think!

21. 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.

22. 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.

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

24. 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.

25. 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.

26. Questions?