Introduction to Machine Learning Week 11 NPTEL Assignment Answers 2025

NPTEL Introduction to Machine Learning Week 11 Assignment Answers 2024

1. Which of the following is/are estimated by the Expectation Maximization (EM) algorithm for a Gaussian Mixture Model (GMM)?

• K (number of components)
• πk (mixing coefficient of each component)
• μk (mean vector of each component)
• Σ_k (covariance matrix of each component)
• None of the above

Answer :- b, c

4. Select the correct statement(s) about the EM algorithm for GMMs.

• In the m^th iteration, the γ(z_nk) values are computed using the paramater estimates computed in the same iteration.
• In the m^th iteration, the γ(z_nk) values are computed using the paramater estimates computed in the (m−1)^th iteration.
• The Σ_k parameter estimates are computed during the E step.
• The π_k parameter estimates are computed during the M step.

Answer :- b, d

5. For questions 5 to 7, use the following data consisting of 8 points (x_i,y_i).

Fit a GMM with 2 components for this data. What are the mixing coefficients of the learned components? (Note: Use the sklearn implementation of GMM with random state = 0. Do not change the other default parameters).

• (0.791, 0.209)
• (0.538, 0.462)
• (0.714, 0.286)
• (0.625, 0.375)

Answer :- d

6. Using the model trained in question 5, compute the log-likelihood of the following points. Which of these points has the highest likelihood of being sampled from the model?

• (2.0, 0.5)
• (-1.0, -0.5)
• (7.5, 8.0)
• (5.0, 5.5)

Answer :- d

7. Let Model A be the GMM with 2 components that was trained in question 5. Using the same data from question 5, estimate a GMM with 3 components (Model B). (Note: Use the sklearn implementation of GMM with random state = 0 and all the other default parameters.)

Select the pair(s) of points that have the same label in Model A but different labels in Model B.

• (1.0, 1.5) and (0.9, 1.6)
• (1.8, 1.2) and (0.9, 1.6)
• (7.8, 9.5) and (8.8, 7.5)
• (7.8, 9.5) and (7.6, 8.0)
• (8.2, 7.3) and (7.6, 8.0)

Answer :- a, c

8. Consider the following two statements.
Statement A: In a GMM with two or more components, the likelihood can attain arbitrarily high values.
Statement B: The likelihood increases monotonically with each iteration of EM.

• Both the statements are correct and Statement B is the correct explanation for Statement A.
• Both the statements are correct, but Statement B is not the correct explanation for Statement A.
• Statement A is correct and Statement B is incorrect.
• Statement A is incorrect and Statement B is correct.
• Both the statements are incorrect.

Answer :- b