Consider the following subset of the Contact Lenses Dataset:

ATTRIBUTES:	POSSIBLE VALUES:
age             {young,pre-presbyopic,presbyopic}
astigmatism     {no,yes}
tear-prod-rate  {reduced,normal}
contact-lenses  {soft,hard,none} <- classification target

• (30 points) Construct the full decision tree for the above Contact Lenses dataset where contact-lenses is the (classification) target attribute. Show all the steps of the calculations and of the construction of your decision tree. For your convenience, the logarithm in base 2 of selected values are provided.

  x	1/2	1/3	1/4	3/4	1/5	2/5	3/5	1/6	5/6	1/7	2/7	3/7	4/7	1
  log2(x)	-1	-1.5	-2	-0.4	-2.3	-1.3	-0.7	-2.5	-0.2	-2.8	-1.8	-1.2	-0.8	0

  
  Unrelated example of decision tree construction
  
  
  (5 points) Use the decision tree you constructed to predict the classification
  (contact-lenses) value of the following test instances. 
  Compute the accuracy of the model on these test data instances. 
  Show your work.
  
  
  young,      no,  reduced, none     your decision tree predicts: ______ 
  pre-pre,    yes, reduced, none     your decision tree predicts: ______
  presbyopic, no,  normal,  soft     your decision tree predicts: ______
  presbyopic, yes, normal,  hard     your decision tree predicts: ______
  
  

Consider the full Contact Lenses Dataset (24 instances):

ATTRIBUTES:	         POSSIBLE VALUES:
age                      {young,pre-presbyopic,presbyopic}
spectacle-prescription:  {myope,hypermetrope}
astigmatism              {no,yes}
tear-prod-rate           {reduced,normal}
contact-lenses           {soft,hard,none} <- classification target

• (30 points) Construct the Naive Bayes classifier over this full dataset. That is, compute all P(A=a | contact-lenses=v) for all predicting attributes A, all attribute A's values a, and all contact-lenses values v. Show all the steps of the calculations.

  Important:Remember to add 1 to all the counts to avoid the problem of having a probability that is equal to 0. For example, note that the number of instances that have astigmatism=yes among the instances that have contact-lenses=soft is equal to 0. Adding 1 to all the counts means that this count [i.e., count (astigmatism=yes | contact-lenses=soft) ] will become 1. Similarly, count(astigmatism=no | contact-lenses=soft) will be 5 + 1 = 6.

  In other words, you need to construct all the conditional probability tables for the Naive Bayes net below based on the 24 data instances:

  

• (5 points) Use the Naive Bayes model you constructed to predict the classification (contact-lenses) value of the following test instances. Compute the accuracy of the model on these test data instances. Show your work.

  young,      myope,        no,  reduced, none     your Naive Bayes model predicts: ______ 
  presbyopic, hypermetrope, yes, normal,  hard     your Naive Bayes model predicts: ______
  
  

Consider the full Contact Lenses Dataset above (24 instances).

• (30 points) Construct all the conditional probability tables for the Bayesian net below based on the 24 data instances:

• (5 points) Use the Bayesian model you constructed to predict the classification (contact-lenses) value of the following test instances. Compute the accuracy of the model on these test data instances. Show your work.

  ASTIGMATISM	TEAR-PROD-RATE	CONTACT-LENSES
  no,  		reduced, 	none     	your Bayes net predicts: ______ 
  yes, 		normal,  	hard     	your Bayes net predicts: ______