Uncertainty and Probabilistic Reasoning - Artificial Intelligence - Lecture Slides, Slides of Artificial Intelligence

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Uncertainty and Probabilistic Reasoning:Lecture 28 of 41

Graphical Models Preliminaries

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Graphical Models of Probability

P =( 20s P ( T , (^) ) · Female P ( F ) ·, PLow, ( L | (^) TNon-Smoker ) · P ( N | T , F ,) · No-Cancer, P ( N | L, N ) · Negative, P ( N | N ) · Negative P ( N | N ))

• • • Conditional IndependenceBayesian (Belief) NetworkMarkov Condition for BBNs (Chain Rule): – – – – – X Example:Acyclic directed graph modelVertices (nodes)Edges (arcs, links) is conditionally independent (CI) from P ( Thunder V : denote events (each a random variable) E (^) : denote conditional dependencies| Rain , Lightning B = ( V, E, ) = (^)  YP ) representing (^) (given Thunder Z iff | PLightning ( X CI assertions | Y , Z ) =)  P ( TX  | over ZR ) for all values of | L  X, Y , and Z
• Example BBN P  X 1 ,X 2 ,  ,Xn   i  n 1 P  Xi|parents  Xi 

 Non Gender  ^ Age Descendant^^ X^ X^12  ^  s^ Exposure-To-Toxins^ Smoking Parents  X^ X^34 ^ Cancer^ X^5^  Descendant^ Serum Calcium^ Lung Tumor^ XX ^67  s

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Semantics of Bayesian Networks

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Markov Blanket

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Evidential Reasoning for Car DiagnosisExample:

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BNJ Core [1]Design

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BNJ Graphical User Interface:Network

© 2004 KSU BNJ Development Team

Network^ ALARM Docsity.com

BNJ Visualization [1]Framework

© 2004 KSU BNJ Development Team Docsity.com

BNJ Visualization [3]Network

© 2004 KSU BNJ Development Team

Network^ Poker Docsity.com

• Scalability – Large networks (50+ vertices, 10+ parents)Features in ProgressCurrent Work:
• Other Visualizations^ – – –^ Very large data sets (10K2 for structure learningConditioning^6 +)
• • BNJ v1-2 portsLazy Evaluation – – Guo’s dissertation algorithms Importance sampling (CABeN) NetworkBarley © 2004 KSU BNJ Development TeamDocsity.com

• Introduction to Probabilistic Reasoning – – Framework: using probabilistic criteria to searchProbability foundationsSummary Points H

• Bayes’s Theorem – – Definition of conditional (posterior) probabilityProduct rule^ •^ •^ Definitions: subjectivist, objectivist; Bayesian, frequentist, logicistKolmogorov axioms

• • MaximumNext Week: Chapter 14, Russell and Norvig – – – Bayes’s Rule and MAP Uniform priors: allow use of MLE to generate MAP hypothesesRelation to version spaces, candidate elimination A Posteriori (MAP) and Maximum Likelihood (ML) Hypotheses

• – Later: Bayesian learning: MDL, BOC, Gibbs, Simple (Naïve) BayesCategorizing text and documents, other applications Docsity.com