CSE 415: Introduction to Artificial Intelligence Winter 2006

Logic

• Given the following axioms in propositional logic:

  1) P -> Q
  2) Q -> R
  3) ~R

  and the conjecture to prove: ~P

  convert the axioms and negated conjecture to conjunctive normal form and show how to prove the conjecture using resolution.

Learning

1. Given the following training set

   f1	f2	C
   1	0	0
   0	0	1
   0	2	2
   0	1	1
   1	0	0
   0	2	2
   0	1	1
   1	0	0

   Compute the information gain of each of the attributes f1 and f2. Which attribute would be chosen at the root of the tree? Show your work, ie. what is the set S and what are the two sets S0 and S1 and the various entropy computations. What will happen at the next level to the node for S0 and the node for S1?

2. What is the purpose of boosting, bagging, and other ensemble methodologies? Are they only for decision trees?

3. How do decision trees and neural nets differ in the ease of humans understanding their decision rules?

Vision

• Given the following image:

  0 0 0 100 100 100
  0 0 0 100 100 100
  0 0 0 100 100 100
  0 0 0 100 100 100
  0 0 0 100 100 100
  

  1. Show how a gradient mask can be used to detect the edge between regions.

  2. Show what the clusters from K-means clustering would be with randomly chosen initial means: 23 45 62 89

• Bring a printed copy of these exercises to class on the due date, Friday March 10. I will check them in and we will go over them on that day. Thus they may NOT be turned in late.