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Transcript march22

CS 4100 Artificial Intelligence
Prof. C. Hafner
Class Notes March 22, 2012
Guidelines for AI Term Project Proposals
• Should be a 2-4 page printable document, including a title for
your project, name and members of your team (with email
addresses), the course, semester, date, etc.
• Introduce the domain and give some preliminary examples of
concepts that will probably be important in your ontology. You
should mention at least one taxonomy and one relationship that
will need to be modeled.
• Justify that planning is useful/necessary in this domain. For
example you might mention a simple (even trivial) kind of
planning that needs to take place.
• Make a start at describing some planning goals/tasks that will
require non-trivial knowledge and reasoning.
• Mention the planning technique you intend to apply to this
(STRIPS operators or formal logic/Situation Calculus).
• It is not necessary to mention or discuss Protégé implementation.
Conditional Probability
• P(X | A,B,C) defined as P(X,A,B,C) / P(A,B,C)
– Assuming Boolean Random Variables
– 8 values of the conditions A B C
– Adding up all P(X,A,B,C) gives us “prior” probability of X
• P(~X | A, B, C) = 1 – P(X | A, B, C)
Conditional Probability
• Chain rules says:
P(A, B, C) = P(A | B, C) P(B, C) =
P(A | B, C) P(B | C) P(C) can also be written
P(A) P(B | A) P(C | A, B)
Bayes rules says: P(X | A,B,C) = P(A,B,C | X) P(X) / P(A,B,C)
*We call α = 1/P(A,B,C) and it applies to all values of X
And write:
P(X | A,B,C) = α P(A,B,C | X) P(X)
Conditional Probability
This is interesting when there is some independence
Conditional independence of 2 variables:
P(X , Y | Z) = P(X | Z) P(Y | Z)
Therefore if A, B, and C are conditionally independent of X
INSTEAD OF P(X | A,B,C) = = α P(A,B,C | X) P(X) =
α P(A |X) P(B | A, X) P(C | A, B, X) P(X)
We get: P(X | A,B,C) = α P(A,B,C | X) P(X) =
α P(A| X) P(B | X) P(C| X) P(X)
How to construct a Bayes Net
Test your understanding: design a Bayes net with plausible
numbers
Calculating using Bayes’ Nets