Birla Institute of Technology & Science, Pilani
Work Integrated Learning Programmes Division
Second Semester 2019-20
M.Tech. (Data Science and Engineering)
Comprehensive Examination (Makeup)
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]
Suppose you receive messages in sequence of bits (0’s and 1’s) with unknown bias θ for 1’s; there is a message sequence as x1, x2, ..., xn of length n is received.
What θ maximizes the likelihood of the data observed (in terms of n) ? Assume that sample x1, x2, ..., xn is from a parametric distribution f (x|θ), where f (x|θ) is the Bernoulli probability mass function with parameter θ. [3 marks]
In context of naive Bayes, what is meant by Laplace smoothing? [1 mark]
Handling extremely low probabilities.
None of these
Make zero probabilities non-zero.
Making probabilities zero.
Why Naïve Bayes algorithm is called so? [2 marks]
Consider fitting a logistic regression model to predict whether a customer will default the bank loan or not given his bank balance, income and whether student/non-student. The optimal model coefficients are: Intercept = -10.86, balance = 0.0057* balance, income = 0.0030 and student = -0.6468. Predict whether a student with balance of Rs.1500 and an income of Rs 40,000 will default or not. [2 marks]
The regression line for predicting weight from height is height=1.51*weight+45.47. Heights is in cm and weights in kg Interpret the equation and find the height of a person whose weight is 100kgs [2+1=3marks]
Question 2. [2+5=7 Marks]
An odd parity generator outputs a ‘1’ when sum of ‘1’s in an input binary sequence is odd.
What are the parity bits P for a binary sequence (x1, x2) of length 2? x1, x2 are either 0 or 1. [2 marks]
Realize an odd parity generator for binary sequence of length 2 using an MLP, with the following logic gate building blocks (with sigmoidal activation function). Show the network architecture with all weights and bias values. [ 1+1+3 = 5 marks]
Question 3. Answer the following questions. [5+5 =10 Marks]
Consider training an AdaBoost classifier using decision stumps on the following data set. Decision stump classifier chooses a constant value c and classifies all points where x > c as one class and other points where x ≤ c as the other class.
1. What is the initial weight that is assigned to each data point? [1 marks]
2. Show the decision boundary for the first decision stump (indicate the positive and negative side of the decision boundary). [2 marks]
3. Circle the point whose weight increases in the boosting process [2 marks]
Suppose you are given the following pairs. You will simulate the k-means algorithm to identify TWO clusters in the data. Suppose you are given initial assignment cluster centre as {cluster1: #1}, {cluster2: #10} – the first data point is used as the first cluster centre and the 10th as the second cluster centre. Please simulate the k-means (k=2) algorithm for one iteration. What are the cluster assignments after one iteration? Assume k-means uses Euclidean distance.
[5 Marks]
Question 4. Answer the following questions. [5 Marks]
Students in a particular class are graded in subjects A, B and C out of 10 points. Based on the information provided in the table below for 8 students, predict using KNN algorithm approach if a student who scored the following grades A 5; B 7; C 6 will pass or fail?
When K = 3?
Question 5. Answer the following questions. [7 Marks]
Solve the below and find the equation for hyper plane using linear Support Vector Machine method.
Positive Points: {(3, 2), (4, 3), (2, 3), (3, -1)}
Negative Points: {(1, 0), (-1, -3), (0, 2), (-1, 2)}
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