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CSCI 121 Special Topics: Bayesian Network Lecture #1: Reasoning Under Uncertainty.
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Transcript of CSCI 121 Special Topics: Bayesian Network Lecture #1: Reasoning Under Uncertainty.
![Page 1: CSCI 121 Special Topics: Bayesian Network Lecture #1: Reasoning Under Uncertainty.](https://reader036.fdocuments.in/reader036/viewer/2022083004/56649dd35503460f94acb1fa/html5/thumbnails/1.jpg)
CSCI 121 Special Topics: Bayesian Network
Lecture #1: Reasoning Under Uncertainty
![Page 2: CSCI 121 Special Topics: Bayesian Network Lecture #1: Reasoning Under Uncertainty.](https://reader036.fdocuments.in/reader036/viewer/2022083004/56649dd35503460f94acb1fa/html5/thumbnails/2.jpg)
UncertaintyTraditional models of reasoning (human; computer) use “all-or-nothing” (discrete) variables and rules:
Hungry(Fido)
Toothache(Simon)
Toothache(X) → Cavity(X)
• Reality is usually more complicated:
Toothache(X) → Cavity(X) 70% of the time
Toothache(X) → Gingivitis(X) 20% of the time
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Uncertainty
In general, all-or-nothing rules fail for three reasons:
1. Laziness – we don't have enough time or resources
list all such rules for a given domain.
2. Theoretical ignorance - we don't have a complete
theory of the domain.
3. Practical ignorance – even with all rules and perfect
theory, we can't make the necessary observations.
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Uncertainty and Rational Decisions
• Utility – how useful is a particular outcome to the agent?
• Probability – how likely is a particular outcome?
• Utility + Probability = Decision theory
• E.g., Lottery: High utility ($$$) x extremely low
probability → bad decision!
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Basic Probability• Prior probability – how likely is something, without any other knowledge? P(cavity) = 0.05
• Conditional (posterior) probability – how likely
is something, once you know something else?
• P(toothache|cavity) = 0.7
• Product Rule: • P(A|B) = P(A & B) / P(B)• P(A &B) = P(A|B) * P(B) = P(B|A)* P(A)
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Basic Probability
• Probability Distribution: All possible values of a given variable, and their probabilities (sum = 1):
•cavity=0.8; gingivitis = 0.1; abcess = 0.05; ? = 0.05
• Joint probability: How likely is it that two things
occur (are observed) together?
• rainy & cloudy = 0.3; cloudy & cool = 0.4
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Axioms of Probability
1) All probabilities are between 0 and 1.
2) Necessarily true propositions (A V ~A) have prob 1; necessarily false (A & ~A) have prob. 0. 3) P(A V B) = P(A) + P(B) – P(A & B)
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Axioms of Probability P(A V B) = P(A) + P(B) – P(A & B)
A BA &
BE.g., in Los Angeles, maybe P(sunny) = 0.8; P(warm) = 0.7. Since P is always less than 1, can't just add 08 + 0.7 to get P(sunny V warm). Need to subtract P(sunny & warm) = 0.6 to get P(sunny V warm) = 0.9.
![Page 9: CSCI 121 Special Topics: Bayesian Network Lecture #1: Reasoning Under Uncertainty.](https://reader036.fdocuments.in/reader036/viewer/2022083004/56649dd35503460f94acb1fa/html5/thumbnails/9.jpg)
Bayes’ Rule
• From the Product Rule:
• P(A|B) = P(A & B) / P(B)
• P(A &B) = P(A|B) * P(B) = P(B|A) * P(A)
Rev. Thomas Bayes (1702-1761)
• We derive Bayes’ Rule by substitution:
• P(A|B) = P(A & B) / P(B) = P(B|A) * P(A) / P(B)
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Bayesian (“Belief”) Nets
Burglary Earthquake
Alarm
JohnCalls MaryCallsA P(J) T .90 F .05
A P(M)T .70F .01
B E P(A)T T .95T F .94F T .29F F .001
P(B).001
P(E).002
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Bayesian Nets Using recently developed techniques (Pearl 1982), we can ask, e.g., “how likely is there to be a burglary, given that John has called?”
Can also learn relationships, creating
“hidden” variables and probability tables,
based on observations.
Current “hot topic” in AI.