Introduction to Machine Learning Nptel Week 11 Answers
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Introduction to Machine Learning Nptel Week 11 Answers (Jan-Apr 2025)
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1) Which of the following is/are estimated by the Expectation Maximization (EM) algorithm for a Gaussian Mixture Model (GMM)?
a) K (number of components)
b) πk (mixing coefficient of each component)
c) μk (mean vector of each component)
d) Σk (covariance matrix of each component)
e) None of the above
2) Which of the following is/are true about the responsibility terms in GMMs? Assume the standard notation used in the lectures.
a) Σkγ(znk)=1∀n
b) Σnγ(znk)=1∀k
c) γ(znk)∈ {0,1} ∀n,k
d) γ(znk)∈ [0,1] ∀n,k
e) πj>πk⟹γ(znj)>γ(znk)∀n
3) What is the update equation for μk in the EM algorithm for GMM?
a) μ(m)k=∑Nn=1γ(znk)|v(m)xn∑Nn=1γ(znk)|v(m−1)
b) μ(m)k=∑Nn=1γ(znk)|v(m−1)xn∑Nn=1γ(znk)|v(m−1)
c) μ(m)k=∑Nn=1γ(znk)|v(m−1)xnN
d) μ(m)k=∑Nn=1γ(znk)|v(m)xnN
Introduction to Machine Learning Nptel Week 11 Answers
4) Select the correct statement(s) about the EM algorithm for GMMs.
a) In the mth iteration, the γ(znk) values are computed using the parameter estimates computed in the same iteration.
b) In the mth iteration, the γ(znk) values are computed using the parameter estimates computed in the (m−1)th iteration.
c) The Σk parameter estimates are computed during the E step.
d) The πk parameter estimates are computed during the M step.
5) 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).
a) (0.791, 0.209)
b) (0.538, 0.462)
c) (0.714, 0.286)
d) (0.625, 0.375)
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?
a) (2.0, 0.5)
b) (-1.0, -0.5)
c) (7.5, 8.0)
d) (5.0, 5.5)
Introduction to Machine Learning Nptel Week 11 Answers
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.
a) (1.0, 1.5) and (0.9, 1.6)
b) (1.8, 1.2) and (0.9, 1.6)
c) (7.8, 9.5) and (8.8, 7.5)
d) (7.8, 9.5) and (7.6, 8.0)
e) (8.2, 7.3) and (7.6, 8.0)
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.
a) Both the statements are correct and Statement B is the correct explanation for Statement A.
b) Both the statements are correct, but Statement B is not the correct explanation for Statement A.
c) Statement A is correct and Statement B is incorrect.
d) Statement A is incorrect and Statement B is correct.
e) Both the statements are incorrect.
Introduction to Machine Learning Nptel Week 11 Answers
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Introduction to Machine Learning Nptel Week 11 Answers