Lecture 20-Probabilistic Inference

Lecture 20-Probabilistic Inference - CS 561 Artificial...

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CS 561: Artificial Intelligence Instructor: Sofus A. Macskassy, [email protected] TAs: Nadeesha Ranashinghe ( [email protected] ) William Yeoh ( [email protected] ) Harris Chiu ( [email protected] ) Lectures: MW 5:00-6:20pm, OHE 122 / DEN Office hours: By appointment Class page: http://www-rcf.usc.edu/~macskass/CS561-Spring2010/ This class will use http://www.uscden.net/ and class webpage - Up to date information - Lecture notes - Relevant dates, links, etc. Course material: [AIMA] Artificial Intelligence: A Modern Approach, by Stuart Russell and Peter Norvig. (2nd ed)
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CS561 - Lecture 20 - Macskassy - Spring 2010 2 Midterm 2 Midterm 2 is next week (April 12) Location: SGM 101 Time: 5pm-6:20pm Covers: Inference in first-order logic Knowledge representation Planning Uncertainty Probabilistic reasoning, inference, reasoning over time Is open-book and open-notes
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CS561 - Lecture 20 - Macskassy - Spring 2010 3 Probabilistic Reasoning [Ch. 14] Bayes Networks Part 1 Syntax Semantics Parameterized distributions Bayes Networks Part2 Exact inference by enumeration Exact inference by variable elimination Approximate inference by stochastic simulation Approximate inference by Markov chain Monte Carlo
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Burglary Earthquake Alarm JohnCalls MaryCalls P(B) 0.001 P(E) 0.002 B E P(A) T T 0.95 T F 0.94 F T 0.29 F F 0.001 A P(J) T 0.90 F 0.05 A P(M) T 0.70 F 0.01 CS561 - Lecture 20 - Macskassy - Spring 2010 4 Alarm example revisited Probabilities derived from prior observations
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Burglary Earthquake Alarm JohnCalls MaryCalls P(B) 0.001 P(E) 0.002 B E P(A) T T 0.95 T F 0.94 F T 0.29 F F 0.001 A P(J) T 0.90 F 0.05 A P(M) T 0.70 F 0.01 What is the probability that the alarm has sounded but neither a burglary nor earthquake has occurred and both John and Mary call?   P j m a b e    CS561 - Lecture 20 - Macskassy - Spring 2010 5
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            0.9 0 0.99 0.7 0.00 .0 0.998 0 2 1 9 06 0 0 P P P m a Pj b P j a Pe be m a a b e       CS561 - Lecture 20 - Macskassy - Spring 2010 6 Burglary Earthquake Alarm JohnCalls MaryCalls P(B) 0.001 P(E) 0.002 B E P(A) T T 0.95 T F 0.94 F T 0.29 F F 0.001 A P(J) T 0.90 F 0.05 A P(M) T 0.70 F 0.01
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CS561 - Lecture 20 - Macskassy - Spring 2010 7 What if we find a new variable? Burglary Earthquake Alarm JohnCalls MaryCalls P(B) 0.001 P(E) 0.002 B S E P(A) T T T 0.98 T T F 0.94 T F T 0.96 T F F 0.95 F T T 0.45 F T F 0.25 F F T 0.29 F F F 0.001 A P(J) T 0.90 F 0.05 A P(M) T 0.70 F 0.01 We find that storms can also set off alarms. We add that into our CPT. Notice that JohnCalls and MaryCalls stay the same since Storms were always there but were just unaccounted for. John and Mary did not change! However, we have better precision at P(A). Storm P(S) 0.1
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CS561 - Lecture 20 - Macskassy - Spring 2010 8 What if we cause a new variable? (or a new variable just occurs) Burglary Earthquake Alarm JohnCalls MaryCalls P(B) 0.001 P(E) 0.002 B C E P(A) T T T 0.98 T T F 0.94 T F T 0.96 T F F 0.95 F T T 0.45 F T F 0.25 F F T 0.29 F F F 0.001 A P(J) T 0.90 F 0.05 A P(M) T 0.70 F 0.01 What if we inject a new cause that was not there before. We pay a crazy guy to set off the alarm frequently, JohnCalls and MaryCalls may no longer be valid since we may have changed the behaviors. For instance the alarm goes
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Lecture 20-Probabilistic Inference - CS 561 Artificial...

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