BITS-WILP-Machine Learning - ML - Comprehensive Examination-Regular - 2019-2020

Birla Institute of Technology & Science, Pilani

Work Integrated Learning Programmes Division

Second Semester 2019-20

M.Tech. (Data Science and Engineering)

Comprehensive Examination (Regular)

Course No.         : DSECLZG565

Course Title         : MACHINE LEARNING  

Nature of Exam        : Open Book 

Weightage         : 40% 

Duration         : 2 Hours  

Date of Exam:           July 12, 2020                            Time of Exam: 10:00 AM – 12:00 PM

Note: Assumptions made if any, should be stated clearly at the beginning of your answer. 

Question 1.        [3+3+2+3=11 marks]       

       

1. Suppose you flip a coin with unknown bias θ; P(x = H | θ) = θ, five times and observe the outcome as HHHHH. 

What is the maximum likelihood estimator for θ? [1 mark]

Would you think this is a good estimator? If not, why not?  [2 marks]

2. A disease has four symptoms and past history of a physician has the following data. Use Naïve Bayes classifier to predict whether patient has disease for new patient data symptoms. [2 marks]                                            

	Symp1	Symp2	Symp3	Symp4	Disease
1	yes	no	mild	yes	no
2	yes	yes	no	no	yes
3	yes	no	strong	yes	yes
4	no	yes	mild	yes	yes
5	no	no	no	no	no
6	no	yes	strong	yes	yes
7	no	yes	strong	no	no
8	yes	yes	mild	yes	yes

For  a new patient
Symp1	Symp2	Symp3	Symp4	Disease
yes	no	mild	yes	?

3. 
   

1. Can logistic regression be applied to multi-class classification problem? 

State true or false [1 mark]

2. Why are log probabilities computed instead of probabilities? [1 mark]

1. To make computation consistent

2. To factor into smaller values of probabilities

3. To factor into larger values of probabilities

4. None of these

4.       1.  In a linear relationship y = m*x+b, y is said to be dependent on x when: [1 mark]

1. m is closer to zero.

2. m is far from zero.

3. b is far from zero.

4. b is closer to zero.

2.    In a linear relationship between y and x, y is not dependent on x when: [1 mark]

1. The coefficient is closer to zero.

2. The coefficient is far from zero.

3. The intercept is far from zero.

4. The intercept is closer to zero.

          3.    In a linear regression model y= w0 + w1*x, if true relationship between y and x is

           y = 7.5 +3.2x, then w0 acts as, [1 mark]

1. Intercepts

2. Coefficients

3. Estimators

4. Residuals

Question 2.                

The following backpropagation network uses an activation function called leaky ReLU that generates output = input, if input >= 0, and 0.1 * input if output < 0.  At a particular iteration, the weights are indicated in the following figure.  Training error is given by E = 0.5*(t-y)2 where t is the target output and y is the actual output from the network. What are the outputs of hidden nodes and actual final output y from the network with x1=x2=1? What will be the weights w31 and w12 in the next iteration with learning rate = 0.1, x1=x2=1, and target output t=0? Assume derivative of activation function = 0 at input = 0, and zero bias at all nodes. [1+1+1+1.5+2.5=7 marks]

Question 3.   

1. Consider training a boosting classifier using decision stumps on the following data set:

1. Circle the examples which will have their weights increased at the end of the first iteration?               [2 marks]

2. How many iterations will it take to achieve zero training error? Explain. [3 marks]

2. A new mobile phone service chain store would like to open 20 service centres in Bangalore.  Each service centre should cover at least one shopping centre and 5,000 households of annual income over 75,000. Design a scalable algorithm that decides locations of service centres by taking all the aforementioned constraints into consideration [5 marks]

Question 4.       

In a clinical trial, height and weight of patients is recorded as shown below in the table. For incoming patient with weight = 58 Kg and Height = 180 cm, classify if patient is Under-weight or Normal using KNN algorithm with When K = 3? [5 marks]                                                                                                                                   

Weight (in Kg)	Height (in cm)	Class
61	190	Under-weight
62	182	Normal
57	185	Under-weight
51	167	Under-weight
69	176	Normal
56	174	Under-weight
60	173	Normal
55	172	Normal
65	172	Normal

Question 5.                       

Considering the following data, Let x1, x2 be the features

                 Positive Points: {(3, 1), (5, 2), (1, 1), (2, 2), (6, -1)}

                 Negative Points: {(-3, 1), (-2, 2), (0, 3), (-3, 4), (-1, 5)}     

        Derive an equation of hyperplane and compute the model parameters. [7 marks]

           

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