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IIT M IMPROVEMENT AN EXAM QIP4 13 July - 13 Jul 2025

MLT Quiz 115 questions40 marks8 MCQ · 5 SA · 2 MSQImprovement / afternoon / QIP4

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Q1MCQ2 marks

How does K-means++ algorithm enhance the initialization process as compared to the standard K-means algorithm?

It ensures the algorithm converges in a fixed number of iterations.
It improves centroid initialization by spreading them out, leading to betterseparated clusters.
It automatically calculates the best value of K.
It removes the need to run the algorithm multiple times.

Q2MCQ2 marks

Q3MCQ4 marks

Q4MCQ4 marks

Q5MCQ3 marks

You are presented with a dataset that has latent variables that influences your data. You are asked to use Expectation-Maximization algorithm to best capture the data. How would you define the steps in the EM (Expectation and Maximization) algorithm?

E-step: Estimate the latent variables in the dataset, M-step: Maximize thelikelihood over the model parameters.
E-step: Estimate the number of latent variables in the dataset, M-step:Maximize the likelihood over the model parameters.
E-step: Estimate the likelihood over the model parameters, M-step: Maximizethe number of latent variables in the dataset.
E-step: Estimate the likelihood over the model parameters, M-step: Maximizethe number of parameters in the model.

Q6MSQ3 marksselect all that apply

Which of the following statements is/are true?

EM algorithm converges to a global optimum.
Lloyd’s algorithm converges to a local optimum.
Poor initialization does not affect the clusters produced by EM algorithm.
Poor initialization leads to a slower convergence of Lloyd’s algorithm.
Lloyd’s algorithm is sensitive to the number of clusters (k).

Q7MSQ3 marksselect all that apply

For a linear regression problem, which among the following are true? Select all that apply.

Gradient descent will converge to a global minimum.
Gradient descent will converge to a local minimum (which is not a globalminimum).
Stochastic gradient descent is guaranteed to converge to a global minimum.
Gradient descent will take lesser number of iterations to converge to a localminimum than stochastic gradient descent.

Q8SA3 marks

Your numeric answer:

Q9SA3 marks

Your numeric answer:

Q10SA2 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

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

Q11MCQ2 marks

Which of the following represents the covariance matrix C?

Q12SA2 marks

What is the variance of the dataset along the first principal component?

Your numeric answer:

Q13MCQ3 marks

Find the residues after projecting the data points onto the first principal component. question figure

Find the residues after projecting the data points onto the first principal component.

Comprehension passage - the questions below it refer to this

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

Q14MCQ3 marks

Q15SA1 mark

Find the mean squared error for the training dataset.

Your numeric answer:

Answer key

Q1 (MCQ, 2 marks): B
Q2 (MCQ, 2 marks): B
Q3 (MCQ, 4 marks): C
Q4 (MCQ, 4 marks): B
Q5 (MCQ, 3 marks): A
Q6 (MSQ, 3 marks): B, D, E
Q7 (MSQ, 3 marks): A, D
Q8 (SA, 3 marks): 0.12 to 0.13
Q9 (SA, 3 marks): 1.147 to 1.150
Q10 (SA, 2 marks): 5250
Q11 (MCQ, 2 marks): B
Q12 (SA, 2 marks): 1
Q13 (MCQ, 3 marks): B
Q14 (MCQ, 3 marks): B
Q15 (SA, 1 marks): 0

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 and K-means++ Algorithms

K-means Algorithm: Iterative algorithm that partitions data into K clusters by minimizing the sum of squared distances to the centroids.
- Objective Function: $F(z_1, \dots, z_n) = \sum_{i=1}^{n} ||x_i - \mu_{z_i}||^2$
K-means++ Algorithm: Enhances K-means by improving centroid initialization to spread them out, leading to better-separated clusters.

2. Kernel Methods

Kernel Transformation: Techniques to transform data into higher-dimensional spaces to make it easier to separate.
- Example: $\phi_1(x) = \frac{10 \phi(x)}{||\phi(x)||_2}$

3. Expectation-Maximization (EM) Algorithm

E-step: Estimate the latent variables in the dataset.
M-step: Maximize the likelihood over the model parameters.

4. Gradient Descent and Stochastic Gradient Descent

Gradient Descent: Optimization algorithm to minimize some function by iteratively moving in the direction of steepest descent.
- Convergence: Converges to a global minimum for linear regression problems.
Stochastic Gradient Descent: A variant of gradient descent that uses a subset of the data to compute the gradient, which can speed up convergence but may not guarantee a global minimum.

5. Principal Component Analysis (PCA)

Principal Components: Directions in the data that have the largest variance.
- Eigenvalue and Eigenvector: For the covariance matrix $X^T X$ , the k-th largest eigenvalue and corresponding eigenvector are used to find the principal components.
- Residues: The remaining data after projecting onto the principal components.
- Variance: The variance of the dataset along the first principal component.

6. Maximum Likelihood Estimation (MLE)

Pareto Distribution: Probability density function $f(x \mid \theta) = \theta x^{-\theta-1}, \quad x \geq 1, \, \theta > 1$ .
- MLE for Pareto Distribution: Given a sample, the maximum likelihood estimator of $\theta$ can be calculated.

7. Linear Regression

Model: $y = w\mathbf{x}, w = \begin{bmatrix} w_1 & w_2 \end{bmatrix}^T$
- Mean Squared Error (MSE): Measure of the average squared difference between the observed and predicted values.