CMU CS 10708 - Structure Learning: the good, the bad, the ugly (38 pages)

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Structure Learning: the good, the bad, the ugly



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Structure Learning: the good, the bad, the ugly

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Pages:
38
School:
Carnegie Mellon University
Course:
Cs 10708 - Probabilistic Graphical Models
Probabilistic Graphical Models Documents

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Koller Friedman Chapter 13 Structure Learning the good the bad the ugly Graphical Model 10708 Carlos Guestrin Carnegie Mellon University October 24th 2005 Announcements Project feedback by e mail soon Where are we Bayesian networks Undirected models Exact inference in GMs Very fast for problems with low tree width Can also exploit CSI and determinism Learning GMs Given structure estimate parameters Maximum likelihood estimation just counts for BNs Bayesian learning MAP for Bayesian learning What about learning structure Learning the structure of a BN Data x1 1 xn 1 x1 M xn M Learn structure and parameters Flu BN encodes conditional independencies Test conditional independencies in data Find an I map Score based approach Finding a structure and parameters is a density estimation task Evaluate model as we evaluated parameters Allergy Sinus Headache Constraint based approach Nose Maximum likelihood Bayesian etc Remember Obtaining a P map September 21st lecture Given the independence assertions that are true for P Obtain skeleton Obtain immoralities From skeleton and immoralities obtain every and any BN structure from the equivalence class Constraint based approach Use Learn PDAG algorithm Key question Independence test Independence tests Statistically difficult task Intuitive approach Mutual information Mutual information and independence Xi and Xj independent if and only if I Xi Xj 0 Conditional mutual information Independence tests and the constraint based approach Using the data D Empirical distribution Mutual information Similarly for conditional MI Use learning PDAG algorithm When algorithm asks X Y U Must check if statistically signifficant Choosing t See reading Score based approach Possible structures Data Flu Allergy Sinus x1 1 xn 1 M x1 xn M Headache Nose Learn parameters Score structure Information theoretic interpretation of maximum likelihood Given structure log likelihood of data Flu Allergy Sinus Headache Nose Information theoretic interpretation of



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