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 You can construct JPTable but often that is overkill