Birla
Institute of Technology & Science, Pilani
Work-Integrated
Learning Programmes Division
First
Semester 2017-2018
Mid-Semester
Test
(EC-2
Regular/ Make-up)
Course No. :
IS ZC464
Course Title : MACHINE LEARNING
Nature of Exam : Closed Book
Duration :
2 Hours
Date of Exam : 24/09/2017 (FN)
Note:
1. Please follow all
the Instructions to Candidates given on the cover page of the answer
book.
2. All parts of a
question should be answered consecutively. Each answer should start from a
fresh page.
3. Assumptions made
if any, should be stated clearly at the beginning of your answer.
Q.1.
Let
data D consists of just n coin flip in which α1
are number of heads and α0 are number of tails [n = α1
+ α0]. Assume that flips are independent and identically distributed
(i.i.d.).
Let X be a binary random variable which
represents a coin.
X= 1; if coin
flips to heads
X=
0; if coin flips to tails
Let Ө refers to the
true probability of head (P(X=1) = Ө)
a) Estimate
Ө by Maximum Likelihood Estimation (MLE). [3]
b) If
Beta distribution is used as prior, show that Maximum a Posteriori Probability Estimation (MAP) of Ө is
Beta distribution:
Q.2.
Consider a training data set {xn,
tn} where n = 1, …, N. A polynomial function of the form
is used to fit the data.
(a) Write
the sum of squared error function without using vector notations. [1]
(b) What
happens if N = 10 and M = 15? Discuss. [1]
(c) What
do you understand by linearly separable data set? [1]
(d) Explain
the following terms in not more than three lines .
(i)
Good generalization. [0.5]
(ii)
Hypothesis set. [0.5]
(iii)
Supervised learning. [0.5]
(iv)
Regularization. [0.5]
IS ZC464 (EC-2
Regular) First Semester
2017-2018 Page 2
Q.3.
Consider
the data set given in the following table:
Outlook
|
Temperature
|
Humidity
|
PlayTennis
|
Overcast
|
Cool
|
Normal
|
Yes
|
Overcast
|
Hot
|
High
|
Yes
|
Overcast
|
Hot
|
High
|
Yes
|
Sunny
|
Cool
|
Normal
|
Yes
|
Overcast
|
Cool
|
Normal
|
No
|
Sunny
|
Hot
|
High
|
No
|
Sunny
|
Hot
|
High
|
No
|
(a) Estimate
all the parameters of Naïve Bayes classifier from the data set given in the
above table. [3]
(b) Using
the above estimated parameters classify the following instance
< Outlook = Sunny, Temperature =Hot,
Humidity =Normal> [1]
(c) Discuss
the difference between generative and discriminative classifiers. Give example for each of them. [2]
Q.4.
Let there are three hypothesis h1,
h2, h3 in the hypothesis space. Suppose that the
posterior probabilities of three hypothesis given the data set, D
are as follows:
P(h1|D)
= 0.4, P(h2|D)
= 0.3, P(h3|D)
= 0.3
Suppose new instance, x is
encountered, which is classified positive by h1, but negative by h2
and h3.
(a) Which
hypothesis is MAP hypothesis? Explain.
[1]
(b) Classify
new instance x using Bayes optimal classifier. [3]
(c) Write
Gibbs Algorithm. [2]
Q.5.
Consider a collection S,
containing positive and negative examples of some target function. Assume it
has two attributes Humidity = {High, Normal} and Wind = {Weak,
Strong}. What is the information Gain for both attributes for the given data?
You can use the notation for Information
Gain of an attribute A as Gain(S, A).
More precisely you need to calculate
Gain(S, Humidity) =? and
Gain(S, Wind) =?
[3 + 3 = 6]
Which attribute is best classifier? [1]
Where + represents the positive examples
and – represents the negative examples.
************
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