Are you looking for NPTEL Introduction to Machine Learning Assignment Week 11 Answers? If yes, you will find the answers to the questions asked in the NPTEL Introduction to Machine Learning quiz exam here. If you are preparing for this exam this article will help you in finding the latest and updated answers.

There is a total of 5 questions related to Gaussian Mixture Models, and Expectation Maximization. The correct answers are marked in Green Color with a tick sign.

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NPTEL Introduction to Machine Learning Assignment Week 11 Answers

1. Given n samples x1, x2, …,xN drawn independently from an Geometric distribution unknown parameter p given by pdf

Pr(X = K) = (1-p)^k-1p for k =1, 2, 3, …, find the MLE of p.

1. PMLE = n/Σⁿ_i=1x_i

2. Suppose we are trying to model a p dimensional Gaussian distribution. What is the actual number of independent parameters that need to be estimated in mean and covariance matrix respectively?

1. None of these

3. Given n samples x₁, x₂, …, x_N drawn independently from a Bionomial distribution unknown parameter p, find the MLE of p. Binomial Distribution is used to model ‘x’ successes in ‘n’ Bernoulli trials. Its p.d.f. is given by:

f(x, n, p) = (ⁿ_x) p^x (1 – p)^n-x

for x = 0, 1, 2, …, n, where (ⁿ_x) = n!/x!(n – x)!

1. PMLE = Σ^N_i=1 X_i/n.N

4. In Gaussian Mixture Models, πi are the mixing coefficients. Select the incorrect conditions that the mixing coefficients need to satisfy for a valid GMM model.

1. -1 ≤ πi ≤ 1, ∀i
2. Σiπi need not be bounded

5. Expectation-Maximization, or the EM algorithm, consists of two steps- E step and the M-step. Using the following notation, select the correct set of equations used at each step of the algorithm.

Notation.
X Known/Given variables/data
Z Hidden/Unknown variables
θ Total set of parameters to be learned
θk Values of all the parameters after stage k
Q(,)The Q-function as described in the lectures

1. E – 𝔼z|x,θ_m-1[log(Pr(X, Z|θ))]
2. M – argmaxθQ (θ, θm-1)

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