Transcript ppt
Methods and Uses of Graph Demoralization Mary McGlohon SIGBOVIK 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. T F Hi Lo .8 .2 .6 .4 Rain Temperature PlayTennis PT ES=T ES=F T .8 .2 F 0 1 EnjoySport Rain Temp PT=T PT=F T Hi .2 .8 T Lo .3 .7 F Hi .4 .6 F Lo .1 .9 Graph Moralization • To convert from directed to undirected graphical model, it is necessary to moralize the graph. We’re living in sin! X1 X3 X2 Unmarried parents = immorality X4 X5 X6 X7 Graph Moralization • To convert from directed to undirected graphical model, it is necessary to moralize the graph. We’re living in sin! X1 X3 X2 Unmarried parents = immorality X4 X5 X6 X7 Graph Moralization • To convert from directed to undirected graphical model, it is necessary to moralize the graph. Saved by the power of Jesus! X1 X3 X2 Marry the parents = moralize X4 X5 X6 X7 Graph Moralization • To convert from directed to undirected graphical model, it is necessary to moralize the graph. X1 X3 X2 Marry the parents = moralize Disclaimer: The moral judgments un-direct edges. represented by Then this preliminary section do not necessarily X4 represent those of the author or the NSF. X5 X6 X7 Graph Demoralization • 3 methods for demoralizing X1 X3 X2 X4 X5 X6 X7 Isolation • Based on social group theory X1 X3 X2 X4 Isolation X1 X3 Choose node(s) to isolate, Remove all edges to/from nodes. X2 X4 X5 X6 X7 Isolation X1 X3 1 graph 5 separate graphs! Probability distribution is totally screwed! X2 X4 X5 X6 X7 Misdirection • Also based on social group theory X1 X3 X2 X4 X5 X6 X7 Misdirection X1 X3 Remove edge, direct it off the page. X2 X4 X5 X6 X7 Misdirection X1 X3 Remove edge, direct it off the page. X2 Confuses probability distribution! Very demoralizing! X4 X5 X6 X7 Disbelief Propagation X1 Condition disbelief on a node, Propagate disbelief through graph. X2 X3 X4 X5 X6 X7 Disbelief Propagation X1 Awww..... X2 X3 X4 X5 X6 X7 Applications • Sating sadistic susceptibility of statisticians More important than you’d think! 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. 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 BayesianFrequentist 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 Machine Learning. (DRAFT) Pink Book Publishing, New York. Questions?