Assignment 4

CMPT 310 - Artificial Intelligence Survey
Assignment 4
Due date: Friday, April 12, 2013
J.P. Delgrande
10 marks March 25, 2013
Important Note: Students must work individually on this, and other CMPT 310, assignments.
You may not discuss the specific questions in this assignment, nor their solutions
with any other student. You may not provide or use any solution, in whole or in part, to or
by another student.
You are encouraged to discuss the general concepts involved in the questions in the context
of completely different problems. If you are in doubt as to what constitutes acceptable
discussion, please ask!
1. (5 marks) Consider the following example:
Aching elbows and aching hands may be the result of arthritis. Arthritis is
also a possible cause of tennis elbow, which in turn may cause aching elbows.
Dishpan hands may also cause aching hands.
(a) Represent these facts in a belief network. Let ar stand for “arthritis”, ah for
“aching hands”, ae for “aching elbow”, te for “tennis elbow”, and dh for “dishpan
hands”.
(b) Suppose the following probabilities are given:
P r(ar) = .001 P r(dh) = .01
P r(ah|ar, dh) = P r(ae|ar, te) = .1
P r(ah|ar, ¬dh) = P r(ae|ar, ¬te) = .99
P r(ah|¬ar, dh) = P r(ae|¬ar, te) = .99
P r(ah|¬ar, ¬dh) = P r(ae|¬ar, ¬te) = .00001
P r(te|ar) = .0001 P r(te|¬ar) = .01
Assume that we are interested in determining whether it is more likely that a
patient has arthritis, tennis elbow, or dishpan hands.
i. With no observations at all, which of the three is most likely a priori?
ii. If we observe that the patient has aching elbows, which is now the most likely?
iii. If we observe that the patient has both aching hands and elbows, which is
the most likely?
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iv. How would your rankings change if there were no causal connection between
tennis elbow and arthritis, where for example
P r(te|ar) = P r(te|¬ar) = .0099
instead of the two values given above?
Please show all of hyour calculations for full marks.
2. (5 marks) Consider an electronics outfit that wants to figure out hom much time to
spend with a customer. Relevant attributes are the person’s age, income, whether they
are a student or not, and their credit rating. The target attribute is whether they will
buy something. You are given the following training data.
Id Age Income Student Rating Purchase
1 < 25 high no ok no
2 < 25 high no good no
3 25 . . . 40 high no ok yes
4 > 40 med no ok yes
5 > 40 low yes ok yes
6 > 40 low yes good no
7 25 . . . 40 low yes good yes
8 < 25 med no ok no
9 < 25 low yes ok yes
10 > 40 med yes ok yes
11 < 25 med yes good yes
12 25 . . . 40 med no good yes
13 25 . . . 40 high yes ok yes
14 > 40 med no good no
The goal is to predict whether a customer will make a purchase, based on the other
attributes.
Construct the optimal decision tree that corresponds to this data. Please show and
explain all steps.
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