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Part II) Short Answer Solve each of the following problems

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Part II) Short Answer

Solve each of the following problems.

1. See the dataset below about Titanic passengers. Room is an independent variable representing the class of room passenger stayed in, first, second, and third. Survive is the dependent variable representing whether the passenger survived the accident. We wish to build a decision tree to determine whether a passenger survived, given room class. Please calculate the total entropy of the data, and the information gain once we use attribute Room as the root node of the decision tree. 

 

Room	Survive
2nd	Yes
1st	No
3rd	Yes
1st	Yes
1st	Yes
3rd	No
2nd	No
3rd	No
1st	Yes
3rd	No
2nd	Yes
3rd	No

Note: 

???_!1 = 0, ???_!

−1      

 

???_!

= −1.6, ???_! 3 = −0.6

 

 

                                   ???_! = −2,                 ???_!

= −0.4

 

???_! 5 = −2.3, ???_! 5 = −1.3, ???_!

= −0.7, ???_!

= −0.3

 

 

 

 

 

1

 

2. See the neural network below, the values of each node in input layer x_i are provided in the plot. All the weights for input layer and hidden layers, w1_ij and w2_ij, are given in the table below. Node x₁ represents gender, where female is 1 and male is 0. Node x₂ represents year of study, where freshman is 1, sophomore is 2, junior is 3, and senior is 4. Node x₃ represents GPA. The output layer represents whether the student will get an A in the new course he/she is taking. Please use the neural network to predict whether a female sophomore student with a GPA of 3.0 will get an A in the course or not. Assume the neural network stops after one iteration of feedforward. 

 

 

 

 

                                           3

 

Weight		Weight
w111 = 0.7		w211 = 0.9
w112 = 0.6		w212 = -0.9
w113 = 0.7		w221 = 0.8
w121 = 0.8		w222 = -0.8
w122 = 0.6		w231 = 0.7
w123 = 0.8		w232 = -0.7
w131 = 0.9
w132 = 0.4
w133 = 0.9

               

2

 

3. See the dataset below. There are four pieces of promotion and insurance information about customers used as evidence attributes: Flight Promotion, Magazine Promotion, Life Insurance, and Credit Insurance. Gender is the class variable. We wish to use Naïve Bayes to predict a customer’s gender, given the information about his/her promotion and insurance. Please find the conditional probability of 

 

P(male | Flight Promotion=No, Magazine Promotion=Yes, Life Insurance=No, Credit Insurance=Yes).

 

Flight Promotion	Magazine Promotion	Life Insurance	Credit Insurance	Gender
Yes	No	No	No	Male
Yes	Yes	Yes	Yes	Female
No	No	No	No	Male
Yes	Yes	Yes	Yes	Male
Yes	No	Yes	No	Female
No	No	No	No	Female
Yes	No	Yes	Yes	Male
No	Yes	No	No	Male
Yes	No	No	No	Male
Yes	Yes	Yes	No	Female

 

               

3