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January 2023 term · Machine Learning Techniques · BSCS2007

MLT Quiz 1: 26 February 2023 (January 2023 term)

The IIT Madras BS Machine Learning Techniques (MLT) Quiz 1 paper sat on 26 Feb 2023, in the January 2023 term: 23 questions for 100 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
23
Marks
100
Duration
120 min
MCQ
9
MSQ
4
Numerical
10
Take as mock testPractise with answers

Updated

Official paper: IIT M DIPLOMA AN2 EXAM QPD2 26 Feb 2023 · No negative marking.

Question 1

+5 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 1 on its own page

Question 2

+5 marksOne correct option
  1. A

    Yes

  2. B

    No

Show answer

Correct answer

  • A

    Yes

Question 2 on its own page

Question 3

+5 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 3 on its own page

Question 4

+5 marksOne correct option
  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • A

    TRUE

Question 4 on its own page

Question 5

+5 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 5 on its own page

Question 6

+5 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • B
Question 6 on its own page

Question 7

+5 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • B
  • D
Question 7 on its own page

Question 8

+5 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • D
Question 8 on its own page

Question 9

+5 marksOne or more correct options

With respect to the Lloyd’s algorithm, choose the correct statements:

Select all that apply.

  1. A

    The partition configurations cannot repeat themselves.

  2. B

    After doing the reassignments (consider at least one point reassigned to the new cluster), we might get the same means for all clusters.

  3. C

    Objective function after making the re-assignments strictly reduces.

  4. D

    Objective function after making the re-assignments may increase.

  5. E

    A change in the objective function's value indicates that the partition configuration has changed.

  6. F

    For partitioning n data points across k partitions, Lloyd's algorithm takes kⁿ iterations to converge.

Show answer

Correct answers

  • A

    The partition configurations cannot repeat themselves.

  • C

    Objective function after making the re-assignments strictly reduces.

  • E

    A change in the objective function's value indicates that the partition configuration has changed.

Question 9 on its own page

Question 10

+5 marksNumerical answer

Consider a dataset of 20 points where the ithi^{th} data-point is given by:

xi=ai⋅[1102]+bi⋅[−1130]\mathbf{x}_i = a_i \cdot \begin{bmatrix} 1 \\ 1 \\ 0 \\ 2 \end{bmatrix} + b_i \cdot \begin{bmatrix} -1 \\ 1 \\ 3 \\ 0 \end{bmatrix}

where, aia_i and bib_i are real numbers such that ∑i=120ai=∑i=120bi=0\sum_{i=1}^{20} a_i = \sum_{i=1}^{20} b_i = 0. Standard PCA is performed on this dataset. If the top two principal components are retained and used to reconstruct the dataset, what is the reconstruction error?

Hint: Think about what happens in R2\mathbb{R}^2 or R3\mathbb{R}^3 for a similar situation and extend this idea to R4\mathbb{R}^4.

Show answer

Correct answer: 0

Question 10 on its own page

Question 11

+5 marksNumerical answer

Consider the following prior for the parameter pp of a Bernoulli distribution:

p∼Beta(3,2)p \sim \text{Beta}(3, 2)

The dataset observed is as follows:

{1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1}\{1,\ 0,\ 1,\ 0,\ 1,\ 1,\ 1,\ 0,\ 0,\ 0,\ 1,\ 1,\ 1\}

What is p^\hat{p}, a point estimate for the parameter of the Bernoulli distribution, if we use the expectation of the posterior as the method of estimation? Enter your answer correct to three decimal places.

Show answer

Correct answer: 0.61 (accepted within ±0.01)

Question 11 on its own page

Question 12

+5 marksNumerical answer

A dataset containing 200 examples in three-dimensional space has been transformed into a higher-dimensional space using a polynomial kernel of degree two. What will be the dimension of the transformed feature space?

Show answer

Correct answer: 10

Question 12 on its own page

Question 13

+2.5 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 5

Question 13 on its own page

Question 14

+2.5 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 20

Question 14 on its own page

Question 15

+5 marksOne correct option

Based on the above data, answer the given subquestions.

  1. A
  2. B
  3. C
  4. D
  5. E
Show answer

Correct answer

  • C
Question 15 on its own page

Question 16

+5 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.33 (accepted within ±0.01)

Question 16 on its own page

Question 17

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 4

Question 17 on its own page

Question 18

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 16.25 (accepted within ±0.02)

Question 18 on its own page

Question 19

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 2

Question 19 on its own page

Question 20

+4 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 2

Question 20 on its own page

Question 21

+4 marksOne correct option

Based on the above data, answer the given subquestions.

What will be the final cluster means?

  1. A
  2. B
  3. C
  4. D
  5. E
Show answer

Correct answer

  • E
Question 21 on its own page

Question 22

+4 marksOne correct option

A k-means++ algorithm with k = 3 was applied to following 2D points:
(0,0),(1,2),(3,1),(4,7),(-1,9),(4,-2)
(0,0) is chosen as the first cluster mean.
Based on the above data, answer the given subquestions.

Which point has the highest probability of being chosen as the 2*^(nd)* cluster mean? Use the manhattan distance to compute the distances.

  1. A

    (3,1)

  2. B

    (4,7)

  3. C

    (-1,9)

  4. D

    (4,-2)

Show answer

Correct answer

  • B

    (4,7)

Question 22 on its own page

Question 23

+4 marksOne correct option

A k-means++ algorithm with k = 3 was applied to following 2D points:
(0,0),(1,2),(3,1),(4,7),(-1,9),(4,-2)
(0,0) is chosen as the first cluster mean.
Based on the above data, answer the given subquestions.

If the point with the highest score is chosen as the 2*^(nd)* cluster mean( answer from previous question ), Which point has the highest probability of being chosen as 3*^(rd)* the cluster mean? Use the manhattan distance to compute the distances.

  1. A

    (3,1)

  2. B

    (4,7)

  3. C

    (-1,9)

  4. D

    (4,-2)

Show answer

Correct answer

  • C

    (-1,9)

Question 23 on its own page