Network-based reasoning COMPSCI 276, Spring 2011 Set 1: - - PowerPoint PPT Presentation

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Network-based reasoning COMPSCI 276, Spring 2011 Set 1: - - PowerPoint PPT Presentation

Oct 22, 2023 148 likes •713 views

Probabilistic Reasoning; Network-based reasoning COMPSCI 276, Spring 2011 Set 1: Introduction and Background Rina Dechter (Reading: Pearl chapter 1-2, Darwiche chapters 1,3) 1 Class Description Instructor: Rina Dechter Days: Tuesday

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Probabilistic Reasoning; Network-based reasoning

COMPSCI 276, Spring 2011 Set 1: Introduction and Background

Rina Dechter

(Reading: Pearl chapter 1-2, Darwiche chapters 1,3)

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Class Description

 Instructor:

Rina Dechter

 Days:

Tuesday & Thursday

 Time:

11:00 - 12:20 pm

 Class page:

http://www.ics.uci.edu/~dechter/courses/ics-275b/spring-11/

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Example of common sense reasoning

 Explosive noise at UCI  Parking in Cambridge  The missing garage door  Years to finish an undergrad degree in

college

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Shooting at UCI

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noise shooting

Fire- crackers

Stud-1 call Vibhav call Anat call Someone calls

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Why uncertainty

 Summary of exceptions

 Birds fly, smoke means fire (cannot enumerate all

exceptions.

 Why is it difficult?

 Exception combines in intricate ways  e.g., we cannot tell from formulas how exceptions

to rules interact:

AC BC

  • A and B - C
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The problem

All men are mortal T All penguins are birds T … Socrates is a man Men are kind p1 Birds fly p2 T looks like a penguin Turn key –> car starts P_n

Q: Does T fly? P(Q)? True propositions Uncertain propositions Logic?....but how we handle exceptions Probability: astronomical

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Managing Uncertainty

 Knowledge obtained from people is almost always

loaded with uncertainty

 Most rules have exceptions which one cannot afford

to enumerate

 Antecedent conditions are ambiguously defined or

hard to satisfy precisely

 First-generation expert systems combined

uncertainties according to simple and uniform principle

 Lead to unpredictable and counterintuitive results  Early days: logicist, new-calculist, neo-probabilist

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Extensional vs Intensional Approaches

 Extensional (e.g., Mycin, Shortliffe,

1976) certainty factors attached to rules and combine in different ways.

 Intensional, semantic-based,

probabilities are attached to set of worlds.

AB: m P(A|B) = m

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Certainty combination in Mycin

A D C B x y z If A then C (x) If B then C (y) If C then D (z) 1.Parallel Combination: CF(C) = x+y-xy, if x,y>0 CF(C) = (x+y)/(1-min(x,y)), x,y have different sign CF( C) = x+y+xy, if x,y<0

  • 2. Series combination…

3.Conjunction, negation Computational desire : locality, detachment, modularity

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The limits of modularity

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P Q P

  • Q

PQ K and P

  • Q

PQ KP K

  • Q

Deductive reasoning: modularity and detachment Plausible Reasoning: violation of locality Wet  rain Wet

  • rain

wet  rain Sprinkler and wet

  • rain?
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Violation of detachment

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Deductive reasoning P  Q K P K

  • Q

Plausible reasoning Wet  rain Sprinkler wet Sprinkler

  • rain?
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Burglery Example

Alarm

Earthquake

Burglery Radio Phone call AB A more credible

  • B more credible

IF Alarm  Burglery A more credible (after radio) But B is less credible Issue: Rule from effect to causes

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Extensional vs Intensional

Uncertainty=truth value Uncertainty = modality Connectives combine certainty weight Connectives combine set of worlds Rules = Procedural license = summary of a problem solving history Rules = constraints on the world = summary of world knowledge Extensional Intensional

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What’s in a rule?

AB (m) CB (n) P(B|A)= p AB (p) Semantic difficulties: Handling exceptions, Retracting conclusions Unidirectional references Incoherent updating Semantic clarity: Syntax mirrors world knowledge Empirically testable parameters Bidirectional Inferences Coherent updating Computational merit: Locality+detachment Computational difficulty: Actions must wait verification of relevance

A and BC (m+n-mn)

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Probabilistic Modeling with Joint Distributions

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Alpha and beta are events

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Burglary is independent of Earthquake

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Earthquake is independent of burglary

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Example

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P(B,E,A,J,M)=?

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Bayesian Networks: Representation

= P(S) P(C|S) P(B|S) P(X|C,S) P(D|C,B) lung Cancer Smoking X-ray Bronchitis Dyspnoea

P(D|C,B) P(B|S) P(S) P(X|C,S) P(C|S)

P(S, C, B, X, D)

Conditional Independencies Efficient Representation

Θ) (G, BN 

CPD:

C B D=0 D=1 0 0 0.1 0.9 0 1 0.7 0.3 1 0 0.8 0.2 1 1 0.9 0.1

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