Question 1
Which of the following options represents matrix A?
Machine Learning Foundations Quiz 2: 4 August 2024 (May 2024 term)
The IIT Madras BS Machine Learning Foundations (MLF) Quiz 2 paper sat on 4 Aug 2024, in the May 2024 term: 15 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.
- 15
- 40
- 120 min
- 10
- 3
- 2
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Correct answer
Question 2
The matrix A is
positive definite.
negative definite.
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negative definite.
Question 3
A is a Hermitian matrix.
A is digonalizable.
All eigenvalue of A real.
A has eigenvalues that are neither real nor purely imaginary.
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Correct answers
A is a Hermitian matrix.
A is digonalizable.
All eigenvalue of A real.
Question 4
Based on the above data, answer the given subquestions.
Which of the following options is true?
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Question 5
Based on the above data, answer the given subquestions.
Which of the following options is true ?
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Question 6
Based on the above data, answer the given subquestions.
Which of the following options is true ?
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Question 7
Which of the following options is/are true?
Any matrix of order n × m is similar to an upper triangular matrix.
If a matrix A is not symmetric, then A^(T)A can not be a symmetric matrix.
If A is a positive definite matrix then A² + I positive definite.
For any matrix A, A^(T)A is orthogonally diagonalizable.
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If A is a positive definite matrix then A² + I positive definite.
For any matrix A, A^(T)A is orthogonally diagonalizable.
Question 8
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Question 9
What is the primary goal of Principal Component Analysis (PCA)?
To find the directions that capture the maximum variance in the data.
To find directions that capture the minimum variance in the data.
To increase the dimensionality of the data.
To reduce the number of data points.
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To find the directions that capture the maximum variance in the data.
Question 10
Based on the above data, answer the given subquestions.
Compute the sample covariance matrix C for the given dataset.
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Question 11
Based on the above data, answer the given subquestions.
Which is the principal direction that is chosen for performing PCA?
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Question 12
Based on the above data, answer the given subquestions.
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Question 13
Which of the following statements about choosing the learning rate in gradient descent is incorrect?
A small learning rate can lead to slow convergence.
A large learning rate can cause the loss function to fluctuate around the minimum.
A large learning rate can cause divergence.
A small learning rate always causes the training to progress very quickly.
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A small learning rate always causes the training to progress very quickly.
Question 14
Consider a function f(x,y) = (x − 1)² + (y − 2)² . Using a gradient descent algorithm, with an initial guess of (0, 0) and learning rate of 0.1, what will be the absolute difference between the value of the function after first and second iteration? Enter the answer correct to three decimal places.
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Correct answer: 1.152 (accepted within ±0.003)
Question 15
The value of a function at point 25 is 5. The values of the function’s first and second order derivatives at this point are 0.1 and -0.002 respectively. What will be the function’s approximate value at the point 25.1? (Enter the answer correct up to three decimal places).
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Correct answer: 5.009 (accepted within ±0.003)