NPTEL Introduction to Machine Learning Week 11 Assignment Answers 2024
1.
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2. The EM algorithm is guaranteed to decrease the value of its objective function on any iteration.
- True
- False
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3. Why might the EM algorithm for GMMs converge to a local maximum rather than the global maximum of the likelihood function?
- The algorithm is not guaranteed to increase the likelihood at each iteration
- The likelihood function is non-convex
- The responsibilities are incorrectly calculated
- The number of components K is too small
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4. What does soft clustering mean in GMMs?
- There may be samples that are outside of any cluster boundary.
- The updates during maximum likelihood are taken in small steps, to guarantee convergence.
- It restricts the underlying distribution to be gaussian.
- Samples are assigned probabilities of belonging to a cluster.
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5.
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6. We apply the Expectation Maximization algorithm to f(D,Z,θ) where D denotes the data, Z denotes the hidden variables and θ the variables we seek to optimize. Which of the following are correct?
- EM will always return the same solution which may not be optimal
- EM will always return the same solution which must be optimal
- The solution depends on the initialization
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7. True or False: Iterating between the E-step and M-step of EM algorithms always converges to a local optimum of the likelihood.
- True
- False
Answer :-
8. The number of parameters needed to specify a Gaussian Mixture Model with 4 clusters, data of dimension 5, and diagonal covariances is:
- Lesser than 21
- Between 21 and 30
- Between 31 and 40
- Between 41 and 50
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