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January 2025 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations End Term: 13 April 2025, Set QDD3 (January 2025 term)

The IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 13 Apr 2025, in the January 2025 term, set QDD3: 14 questions for 40 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
14
Marks
40
Duration
180 min
MCQ
2
MSQ
7
Numerical
5
Take as mock testPractise with answers

Updated

Official paper: IIT M DIPLOMA AN EXAM QDD3 13 Apr 2025 · No negative marking.

Question 1

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

Correct answer

  • A
Question 1 on its own page

Question 2

+3 marksOne correct option

The random variable yy is being transformed according to the measurement mapping:

z=Cy+ϵ,z = Cy + \epsilon,

where:

  • z∈Rdz \in \mathbb{R}^d,
  • C∈Rd×nC \in \mathbb{R}^{d \times n},
  • ϵ∼N(0,σ2Id)\epsilon \sim \mathcal{N}(0, \sigma^2 I_d) is independent Gaussian (measurement) noise.

Which of the following represents the conditional probability distribution p(z∣y)p(z \mid y)?

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

Correct answer

  • A
Question 2 on its own page

Question 3

+3 marksOne or more correct options

Which of the following statements about singular value decomposition (SVD) is/are true?

Select all that apply.

  1. A

    Singular value decomposition is possible only for a square matrix.

  2. B

    Singular value decomposition is possible only for a symmetric matrix.

  3. C

    The singular values of a matrix are always non-negative.

  4. D

    The singular values of matrices A and A^(T) are the same.

Show answer

Correct answers

  • C

    The singular values of a matrix are always non-negative.

  • D

    The singular values of matrices A and A^(T) are the same.

Question 3 on its own page

Question 4

+3 marksOne or more correct options

In the context of Linear Algebra, which of the following statements about Principal Component Analysis (PCA) is/are true?

Select all that apply.

  1. A

    The principal components of a matrix are given by the eigenvectors of its covariance matrix.

  2. B

    The principal components of a matrix are given by the singular values of its covariance matrix.

  3. C

    PCA finds the principal components by maximizing the variance along each component.

  4. D

    The principal components form a basis that is not necessarily orthogonal.

Show answer

Correct answers

  • A

    The principal components of a matrix are given by the eigenvectors of its covariance matrix.

  • C

    PCA finds the principal components by maximizing the variance along each component.

Question 4 on its own page

Question 5

+3 marksOne or more correct options

Which of the following options is/are true?

Select all that apply.

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

Correct answers

  • A
  • B
Question 5 on its own page

Question 6

+3 marksOne or more correct options

Which of the following options is/are true ?

Select all that apply.

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

Correct answers

  • B
  • C
Question 6 on its own page

Question 7

+3 marksOne or more correct options

Select all that apply.

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

Correct answers

  • A
  • D
Question 7 on its own page

Question 8

+3 marksNumerical answer
Show answer

Correct answer: 12

Question 8 on its own page

Question 9

+3 marksNumerical answer
Show answer

Correct answer: 0.2

Question 9 on its own page

Question 10

+4 marksNumerical answer
Show answer

Correct answer: 46

Question 10 on its own page

Question 11

+2 marksNumerical answer
Show answer

Correct answer: -0.2

Question 11 on its own page

Question 12

+2 marksOne or more correct options

Consider an optimization problem

min⁡f(x,y,z,w)=x2+y2+z2+w2+1\min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1

subject to constraints:

x+y+z+w=1x + y + z + w = 1

w≤δw \le \delta

Let the Lagrangian function is,

L(x,α,β)=x2+y2+z2+w2+1+α(1−x−y−z−w)+β(w−δ)L(x, \alpha, \beta) = x^2 + y^2 + z^2 + w^2 + 1 + \alpha(1 - x - y - z - w) + \beta(w - \delta)

Based on the above data, answer the given subquestions.

Which of the following statements correctly represent the Karush-Kuhn-Tucker (KKT) conditions for the given optimization problem?

Select all that apply.

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

Correct answers

  • A
  • C
Question 12 on its own page

Question 13

+3 marksOne or more correct options

Consider an optimization problem

min⁡f(x,y,z,w)=x2+y2+z2+w2+1\min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1

subject to constraints:

x+y+z+w=1x + y + z + w = 1

w≤δw \le \delta

Let the Lagrangian function is,

L(x,α,β)=x2+y2+z2+w2+1+α(1−x−y−z−w)+β(w−δ)L(x, \alpha, \beta) = x^2 + y^2 + z^2 + w^2 + 1 + \alpha(1 - x - y - z - w) + \beta(w - \delta)

Based on the above data, answer the given subquestions.

Which of the following statements are correct based on the KKT conditions and the solution to the optimization problem?

Select all that apply.

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

Correct answers

  • A
  • C
Question 13 on its own page

Question 14

+3 marksNumerical answer

Consider an optimization problem

min⁡f(x,y,z,w)=x2+y2+z2+w2+1\min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1

subject to constraints:

x+y+z+w=1x + y + z + w = 1

w≤δw \le \delta

Let the Lagrangian function is,

L(x,α,β)=x2+y2+z2+w2+1+α(1−x−y−z−w)+β(w−δ)L(x, \alpha, \beta) = x^2 + y^2 + z^2 + w^2 + 1 + \alpha(1 - x - y - z - w) + \beta(w - \delta)

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.25

Question 14 on its own page