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January 2024 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations Quiz 1: 25 February 2024 (January 2024 term)

The IIT Madras BS Machine Learning Foundations (MLF) Quiz 1 paper sat on 25 Feb 2024, in the January 2024 term: 11 questions for 40 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
11
Marks
40
Duration
120 min
MCQ
6
MSQ
4
Numerical
1
Take as mock testPractise with answers

Updated

Official paper: IIT M DIPLOMA AN2 EXAM QDD2 25 Feb 2024 · No negative marking.

Question 1

+4 marksOne correct option

Find the row space of matrix A.

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

Correct answer

  • B
Question 1 on its own page

Question 2

+3 marksOne correct option

Find the column space of matrix A.

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

Correct answer

  • A
Question 2 on its own page

Question 3

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

Correct answer

  • B
Question 3 on its own page

Question 4

+3 marksOne correct option
  1. A

    2.1

  2. B

    2.003125

  3. C

    2.031

  4. D

    1.9968

Show answer

Correct answer

  • B

    2.003125

Question 4 on its own page

Question 5

+4 marksOne correct option

Find the best fit line for the dataset given below using least squares method.

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

Correct answer

  • B
Question 5 on its own page

Question 6

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

Correct answer

  • A
Question 6 on its own page

Question 7

+3 marksOne or more correct options

Which of the following is/are supervised learning task(s)?

Select all that apply.

  1. A

    Predicting future sales of a product based on the past sales data.

  2. B

    Reducing the dimensionality of images while retaining essential features, enabling efficient storage and transmission.

  3. C

    Recognizing and interpreting handwritten characters or words, often used in digit recognition or reading handwritten text.

  4. D

    Categorizing text documents into predefined classes, such as spam or non- spam emails.

Show answer

Correct answers

  • A

    Predicting future sales of a product based on the past sales data.

  • C

    Recognizing and interpreting handwritten characters or words, often used in digit recognition or reading handwritten text.

  • D

    Categorizing text documents into predefined classes, such as spam or non- spam emails.

Question 7 on its own page

Question 8

+4 marksOne or more correct options

Select all that apply.

  1. A

    Eigenvalues of A are 1, 2, and 3.

  2. B

    Eigenvalues of A are 1, 2, and 2.

  3. C

    Eigenvalues of B are 2, 20, and 78.

  4. D

    Matrix B is diagonalizable.

Show answer

Correct answers

  • A

    Eigenvalues of A are 1, 2, and 3.

  • D

    Matrix B is diagonalizable.

Question 8 on its own page

Question 9

+4 marksOne or more correct options

Let A and B be symmetric matrices such that AB = BA. Then which of the following options is/are true?

Select all that apply.

  1. A

    AB is a symmetric matrix.

  2. B

    AB is orthogonally diagonalizable.

  3. C

    BA has real eigenvalues.

  4. D

    AB is not a symmetric matrix.

Show answer

Correct answers

  • A

    AB is a symmetric matrix.

  • B

    AB is orthogonally diagonalizable.

  • C

    BA has real eigenvalues.

Question 9 on its own page

Question 10

+4 marksOne or more correct options

Select all that apply.

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

Correct answers

  • A
  • C
  • D
Question 10 on its own page

Question 11

+4 marksNumerical answer

Consider an encoder-decoder pair used for dimensionality reduction, where the encoder function is denoted as f(x1,x2,x3)=(x1+x2−x3,x1+x3)f(x_1, x_2, x_3) = (x_1 + x_2 - x_3, x_1 + x_3) and the decoder function is denoted as g(u)=(u1,u2,u1+u2)g(u) = (u_1, u_2, u_1 + u_2)

Compute the reconstruction error (R(f,g)=1n∑i=1n∥Xi−g(f(Xi))∥2)\left(R(f, g) = \dfrac{1}{n} \sum\limits_{i=1}^{n} \|X_i - g(f(X_i))\|^2\right) for the following dataset:

X1=[1,2,3],    X2=[0,2,2],    X3=[1,0,−1]X_1 = [1, 2, 3], \;\; X_2 = [0, 2, 2], \;\; X_3 = [1, 0, -1]

Enter the answer correct to two decimal places.

Show answer

Correct answer: 3.16 (accepted within ±0.04)

Question 11 on its own page