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IIT M DIPLOMA AN3 EXAM QPD3 29 Oct 2023 - 29 Oct 2023

MLT Quiz 113 questions50 marks6 MCQ · 5 SA · 2 MSQDiploma / QPD3

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Q1MCQ4 marks

μ1 = (2.5, 2.5)
μ1 = (4.5, 4.5)
μ1 = (3, 3)
μ1 = (5.5, 5.5)

Q2MCQ4 marks

C1
C2
C3
It remains in the same cluster as in the first iteration

Q3MSQ4 marksselect all that apply

Which of the following statements are true regarding applying standard PCA on a centered dataset?

The variance of the dataset along the first principal component is maximum.
Eigenvectors are always orthogonal to each other in PCA.
The first principal component is the eigenvector corresponding to the largesteigenvalue of the covariance matrix.
The first principal component is the eigenvector corresponding to the smallesteigenvalue of the covariance matrix.

Q4SA4 marks

Consider a dataset that has 200 data-points, each of which is either a zero or one. The Bernoulli distribution is used to model this data. If the MLE estimate for the parameter p of the Bernoulli distribution is 0.3, how many zeros does the dataset have?

Your numeric answer:

Q5SA4 marks

Your numeric answer:

Q6SA4 marks

Your numeric answer:

Q7SA4 marks

Your numeric answer:

Q8SA3 marks

Enter your answer correctly up to two decimals question figure

Your numeric answer:

Comprehension passage - the questions below it refer to this

A k-means++ algorithm with k= 3 was applied to the following 2D points: (2, 2), (3, 3), (4, 4), (10, 10), (12, 12), (13, 13) (2, 2) is chosen as the first cluster mean. Based on the above data, answer the given subquestions.

Q9MCQ4 marks

Which point has the highest probability of being chosen as the 2nd cluster mean? Use the Manhattan distance to compute the distances.

(4, 4)
(12, 12)
(10, 10)
(13, 13)

Q10MCQ4 marks

Let’s assume that (3, 3), (10, 10), and (12, 12) are the cluster means. You introduce a new data point, (−5, 10). Which cluster mean is the data point (−5, 10) closest to when using the Euclidean distance method?

(3, 3)
(10, 10)
(12, 12)
None of these

Comprehension passage - the questions below it refer to this

Based on the above data, answer the given subquestions. question figure

Q11MSQ4 marksselect all that apply

Which of the following statements are true?

Q12MCQ4 marks

Which of the following matrices helps in transforming the eigenvectors of K to the eigenvectors of C?

Q13MCQ3 marks

Suppose that the 95% of the variance of the data is captured using d − 1 eigenvectors. This implies that

Answer key

Q1 (MCQ, 4 marks): C
Q2 (MCQ, 4 marks): A
Q3 (MSQ, 4 marks): A, B, C
Q4 (SA, 4 marks): 140
Q5 (SA, 4 marks): 625
Q6 (SA, 4 marks): 4
Q7 (SA, 4 marks): 0.3 to 0.4
Q8 (SA, 3 marks): 0.2 to 0.3
Q9 (MCQ, 4 marks): C
Q10 (MCQ, 4 marks): B
Q11 (MSQ, 4 marks): B, C, E
Q12 (MCQ, 4 marks): A
Q13 (MCQ, 3 marks): B

Concepts this paper tests

Auto-generated summary from the source site. Handy as a checklist; the lessons above explain each idea from scratch.

Summary of Core Topics, Concepts, Principles, and Equations

1. K-Means Clustering

Concepts: Cluster centroids, sum of squared distances, cluster assignment.
Principles: Minimize the sum of squared distances between data points and their assigned centroids.
Equations:

\mu_k = \frac{\sum x_i \mathbb{1}(z_i = k)}{\sum \mathbb{1}(z_i = k)}

where $x_i$ is the $i^{\text{th}}$ data point and $z_i$ is the cluster assignment for $x_i$ .

2. Principal Component Analysis (PCA)

Concepts: Eigenvalues, eigenvectors, covariance matrix, variance, principal components.
Principles: PCA transforms data to a new coordinate system where the greatest variance lies on the first axis (first principal component), the second greatest variance on the second axis, and so on.
Equations:

C = \frac{1}{n} XX^T

f(\mathbf{w}) = \mathbf{w}^T C \mathbf{w}

where $C$ is the covariance matrix and $\mathbf{w}$ is the unit vector pointing in the direction of the line.

3. Bernoulli Distribution and Maximum Likelihood Estimation (MLE)

Concepts: Bernoulli distribution, MLE, parameter estimation.
Principles: MLE estimates the parameters of a statistical model by maximizing the likelihood function.
Equations:

\hat{p} = \frac{\text{number of successes}}{\text{total number of trials}}

4. Gaussian Mixture Models (GMM) and Expectation-Maximization (EM) Algorithm

Concepts: Mixture models, EM algorithm, posterior probabilities.
Principles: GMM uses the EM algorithm to find the parameters of the Gaussian distributions that best fit the data.
Equations:

\pi_k = \frac{\sum_{i=1}^{n} \lambda_k^i}{n}

where $\lambda_k^i$ is the posterior probability of data point $i$ belonging to cluster $k$ .

5. Bayesian Estimation

Concepts: Prior distribution, posterior distribution, Beta distribution.
Principles: Bayesian estimation updates the prior distribution with observed data to obtain the posterior distribution.
Equations:

\text{Posterior mean} = \frac{\alpha + \text{number of successes}}{\alpha + \beta + \text{total number of trials}}

where $\alpha$ and $\beta$ are the parameters of the Beta prior distribution.

6. K-Means++ Algorithm

Concepts: Initialization of cluster centroids, distance metrics (Manhattan distance, Euclidean distance).
Principles: K-Means++ improves the initialization of cluster centroids to speed up convergence and improve the quality of clustering.
Equations: Distance metrics such as Manhattan distance and Euclidean distance.