Probabilistic Reasoning; Network-based reasoning COMPSCI 276, Spring - - PowerPoint PPT Presentation

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Probabilistic Reasoning; Network-based reasoning COMPSCI 276, Spring - - PowerPoint PPT Presentation

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Probabilistic Reasoning; Network-based reasoning COMPSCI 276, Spring 2013 Set 1: Introduction and Background Rina Dechter (Reading: Pearl chapter 1-2, Darwiche chapters 1,3) 1 Class Description n Instructor: Rina Dechter n Days:

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Probabilistic Reasoning; Network-based reasoning

COMPSCI 276, Spring 2013 Set 1: Introduction and Background

Rina Dechter

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

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Class Description

n Instructor: Rina Dechter n Days:

Tuesday & Thursday

n Time:

11:00 - 12:20 pm

n Class page:

n

http://www.ics.uci.edu/~dechter/courses/ics-275b/spring-13/

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Outline

n Why uncertainty? n Basics of probability theory and

modeling

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Why Uncertainty?

n

AI goal: to have a declarative, model-based, framework that allow computer system to reason.

n

People reason with partial information

n

Sources of uncertainty:

n

Limitation in observing the world: e.g., a physician see symptoms and not exactly what goes in the body when he performs diagnosis. Observations are noisy (test results are inaccurate)

n

Limitation in modeling the world,

n

maybe the world is not deterministic.

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Example of common sense reasoning

n Explosive noise at UCI n Parking in Cambridge n The missing garage door n 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 what is the likelihood that there was a criminal activity if S1 called? What is the probability that someone will call the police?

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Why uncertainty

n Summary of exceptions

n Birds fly, smoke means fire (cannot enumerate all

exceptions.

n Why is it difficult?

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

to rules interact:

AàC BàC

  • A and B -à 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

n Knowledge obtained from people is almost always

loaded with uncertainty

n Most rules have exceptions which one cannot afford

to enumerate

n Antecedent conditions are ambiguously defined or

hard to satisfy precisely

n First-generation expert systems combined

uncertainties according to simple and uniform principle

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

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Extensional vs Intensional Approaches

n Extensional (e.g., Mycin, Shortliffe,

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

n Intensional, semantic-based,

probabilities are attached to set of worlds.

Aà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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Pà Q P

  • Q

PàQ K and P

  • Q

PàQ KàP K

  • Q

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

  • rain

wet à rain Sprinkler and wet

  • rain?
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Violation of detachment

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Deductive reasoning P à Q Kà P K

  • Q

Plausible reasoning Wet à rain Sprinkler àwet Sprinkler

  • rain?
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Burglery Example

Alarm

Earthquake

Burglery Radio Phone call AàB A more credible

  • B more credible

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

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Probabilistic Modeling with Joint Distributions

n All frameworks for reasoning with

uncertainty today are “intentional” model-based. All are based on the probability theory implying calculus and semantics.

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Outline

n Why uncertainty? n Basics of probability theory and

modeling

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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