19 Aug PROBLEMS

Instructions

You must make your own calculations and you must show your calculations in the answer document. Insufficient calculation steps will result in reduced points earned.

 

Imbalanced Classifiers

1. Begin by writing the formula for each calculation, then show your steps to arrive at your answer.

a. Calculate Accuracy

b. Precision

c. Recall

d. F- Measure

 

2. Begin by writing the formula for each calculation, then show your steps to arrive at your answer.

a. Calculate Accuracy

b. Precision

c. Recall

d. F- Measure

 

Bayes Theorem

3. (a) Suppose the fraction of undergraduate students who smoke is 15% and

the fraction of graduate students who smoke is 23%. If one-fifth of the college students are graduate students and the rest are undergraduates, what is the probability that a student who smokes is a graduate student?

Answer

(b) Given the information in part (a), is a randomly chosen college student

more likely to be a graduate or undergraduate student?

Answer

(c) Repeat part (b) assuming that the student is a smoker.

Answer:

(d) Suppose 30% of the graduate students live in a dorm but only 10% of

the undergraduate students live in a dorm. If a student smokes and lives in the dorm, is he or she more likely to be a graduate or undergraduate student? You can assume independence between students who live in a dorm and those who smoke.

Answer:

 

Bayes Theorem

4. Consider the data set below.

a) Estimate the conditional probabilities for (P(A|+), P(B|+), P(C|+), P(A|-). P(B|-), P(C|-)

(b) Use the estimate of conditional probabilities given in the previous question to predict the class label for a test sample (A =0, B =1, C =0) using the naïve Bayes approach.

 

1. Consider a binary classification problem with the following set of attributes and attribute values:

• Air Conditioner = {Working, Broken}

• Engine = {Good, Bad}

• Mileage = {High, Medium, Low}

• Rust = {Yes, No}

Suppose a rule-based classifier produces the following rule set:

(a) Are the rules mutually exclusive?

Answer:

(b) Is the rule set exhaustive?

Answer:

(c) Is ordering needed for this set of rules?

Answer:

(d) Do you need a default class for the rule set?

Answer:

 

2. Consider a training set that contains 100 positive examples and 400 negative examples. For each of the following candidate rules.

R1: A -→ + (covers 4 positive and 1 negative examples)

R2: B -→ + (covers 30 positive and 10 negative examples)

R3: C -→ + (covers 100 positive and 90 negative examples)

Note: The rules do not cover the entire training set. This is not an exhaustive rule set.

a. Determine which is the best and worst candidate rule according to Rule accuracy.

Answer:

b. Determine which is the best and worst candidate rule according to FOIL’s information gain.

Review of FOIL’s Information Gain

R0: {} => class (initial rule)

R1: {A} => class (rule after adding conjunct)

Gain(R0, R1) = t [ log (p1/(p1+n1)) – log (p0/(p0 + n0)) ]

where…
t (total) number of positive instances covered by both R0 and R1

p0 number of positive instances covered by R0

n0 number of negative instances covered by R0

p1 number of positive instances covered by R1

n1 number of negative instances covered by R1

Answer:

 

3. Consider the one-dimensional data set shown below.

Data set for Exercise 3.

 

x

0.5

3.0

4.5

4.6

4.9

5.2

5.3

5.5

7.0

9.5

 

y – 1st

 

y – 2nd

 

y – 3rd

 

y – 4th

a. Place the indicated symbol ( + or – ) into each cell for the purpose of classifying the data point x =5.0 according to its 1-, 3-, 5-, and 9-nearest neighbors (using majority vote).

Answer:

Number of data points  symbol to be used/inserted into y row

1st Row 1-nearest neighbor  +

2nd Row 3-nearest neighbor  –

3rd Row 5-nearest neighbor +

4th Row 9-nearest neighbor –