Figure from the original question paper

(B) Option figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the original question paper

(B) To ensure that unseen categorical feature values receive small but nonzero probabilities.

(A) To prevent numerical errors when calculating the variance of Gaussian features.

(C) To strengthen the model’s predictions by increasing the weight of certain features.

(D) To balance the likelihood values of all features before computing posterior probabilities.

Figure from the original question paper

(B) It computes the similarity between data points in a transformed feature space.

(C) It allows the model to capture non-linear relationships by mapping data to a higher-dimensional space.

(A) It ensures that the regression model remains linear.

(D) It helps in reducing the variance of the model.

(E) It minimizes the loss function in regression problems.

Figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(B) Option figure from the original question paper

(D) Option figure from the original question paper

Consider the following 2D data points along with its labels: | x | y | |---|---| | \begin{bmatrix} 1 & 1 \end{bmatrix}^T | 1 | | \begin{bmatrix} 1 & -1 \end{bmatrix}^T | 1 | | \begin{bmatrix} 2 & 1 \end{bmatrix}^T | 1 | | \begin{bmatrix} 2 & 2 \end{bmatrix}^T | 1 | | \begin{bmatrix} 2 & -2 \end{bmatrix}^T | 0 | | \begin{bmatrix} 3 & -3 \end{bmatrix}^T | 0 | | \begin{bmatrix} 4 & -1 \end{bmatrix}^T | 1 | Based on the above data, answer the given subquestions. Is it possible to reduce the cross-validation error obtained in the previous question by changing the label of certain points?

(C) Cannot conclude from the given information.

January 2025 term · Machine Learning Techniques · BSCS2007

Machine Learning Techniques Quiz 2: 16 March 2025 (January 2025 term)

The IIT Madras BS Machine Learning Techniques (MLT) Quiz 2 paper sat on 16 Mar 2025, in the January 2025 term: 14 questions for 40 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions: 14
Marks: 40
Duration: 120 min
MCQ: 6
MSQ: 2
Numerical: 6

Take as mock test Practise with answers

Updated 25 Sept 2026

Official paper: IIT M DIPLOMA AN EXAM QDD2 16 Mar 2025 · No negative marking.

Question 1

+3 marksOne correct option

Below is the constrained version of the ridge regression optimization problem:

$\min_{w \in \mathbb{R}} \sum_{i=1}^{n} (w^T x_i - y_i)^2$

$\text{subject to } ||w||^2 \leq \theta.$

Following are the weight vectors to be considered, along with the mean squared error (MSE) produced by each:

$w_1 = \begin{bmatrix} 1 & 1 & 1 & 1 \end{bmatrix}^T$ , $MSE = 2$
$w_2 = \begin{bmatrix} 0 & 2 & 1 & 3 \end{bmatrix}^T$ , $MSE = 7$
$w_3 = \begin{bmatrix} 1 & 2 & 0 & 1 \end{bmatrix}^T$ , $MSE = 1$
$w_4 = \begin{bmatrix} 2 & 1 & 1 & 2 \end{bmatrix}^T$ , $MSE = 8$

If $\theta = 10$ , which of the following weight vectors will be selected as the final weight vector by ridge regression?

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Correct answer

Question 1 on its own page

Question 2

+3 marksOne correct option

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Correct answer

Question 2 on its own page

Question 3

+2 marksOne correct option

p is the proportion of points with label 1 in some node in a decision tree. Which of the following statements are true?

A
As the value of p increases from 0 to 1, the impurity of the node increases.
B
As the value of p increases from 0 to 1, the impurity of the node decreases.
C
The impurity of the node does not depend on p.
D
p = 0.5 correspond to the case of maximum impurity.

Show answer

Correct answer

D
p = 0.5 correspond to the case of maximum impurity.

Question 3 on its own page

Question 4

+2 marksOne correct option

A
To prevent numerical errors when calculating the variance of Gaussian features.
B
To ensure that unseen categorical feature values receive small but nonzero probabilities.
C
To strengthen the model’s predictions by increasing the weight of certain features.
D
To balance the likelihood values of all features before computing posterior probabilities.

Show answer

Correct answer

B
To ensure that unseen categorical feature values receive small but nonzero probabilities.

Question 4 on its own page

Question 5

+4 marksOne correct option

Consider the following feature ( $x$ ) along with its label ( $y$ ):

$x$	$y$
1	1
$-1$	1
2	1
$-2$	0
3	0
4	1

If you are provided with the following two questions, which one should you choose for the first(top) node of the decision tree?

(a) $x \leq -2$
(b) $x \leq -1$

Recall: Information gain $= \text{Entropy}(D) - \gamma \text{Entropy}(D_{Yes}) - (1 - \gamma) \text{Entropy}(D_{No})$

Use the following values if required:
$\log_2(3/4) = -0.41, \log_2(4/5) = -0.32, \log_2(1/5) = -2.32, \log_2(1/4) = -2, \log_2(1/2) = -1.$

A
(a)
B
(b)
C
Insufficient information

Show answer

Correct answer

A
(a)

Question 5 on its own page

Question 6

+3 marksOne or more correct options

Select all that apply.

A
It ensures that the regression model remains linear.
B
It computes the similarity between data points in a transformed feature space.
C
It allows the model to capture non-linear relationships by mapping data to a higher-dimensional space.
D
It helps in reducing the variance of the model.
E
It minimizes the loss function in regression problems.

Show answer

Correct answers

B
It computes the similarity between data points in a transformed feature space.
C
It allows the model to capture non-linear relationships by mapping data to a higher-dimensional space.

Question 6 on its own page

Question 7

+3 marksOne or more correct options

Select all that apply.

Show answer

Correct answers

Question 7 on its own page

Question 8

+4 marksNumerical answer

Consider a kernel regression problem on the following dataset with two features:

$\{(x_1, y_1), (x_2, y_2), (x_3, y_3)\}$

where:

$x_1 = \begin{bmatrix} 1 & 2 \end{bmatrix}^T, y_1 = 3, \quad x_2 = \begin{bmatrix} 2 & 3 \end{bmatrix}^T, y_2 = 5, \quad x_3 = \begin{bmatrix} 3 & 4 \end{bmatrix}^T, y_3 = 7$

The kernel function is given as:

$K(x, x') = (1 + x^\top x')^2$

and the optimal coefficients $\alpha_i$ are given as:

$\alpha = \begin{bmatrix} 0.5 & 1.0 & 1.5 \end{bmatrix}^T.$

Then, what will be the predicted value for the data point $\begin{bmatrix} 2 & 2 \end{bmatrix}^T$ ?

Show answer

Correct answer: 483

Question 8 on its own page

Question 9

+4 marksNumerical answer

Consider a Naive Bayes problem with three features, $f_1, f_2$ and $f_3$ for a binary classification problem. We have a total of 6 training samples given in the table below:

Sample	$f_1$	$f_2$	$f_3$	$y$
$x_1$	0	1	1	0
$x_2$	1	0	1	0
$x_3$	0	0	1	0
$x_4$	0	0	0	1
$x_5$	1	0	1	1
$x_6$	0	1	0	1

For $x_{test} = \begin{bmatrix} 1 & 1 & 0 \end{bmatrix}^T$ , what output would Naive Bayes model predict assuming that no Laplacian smoothing has been done as part of the algorithm?

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Correct answer: 1

Question 9 on its own page

Question 10

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 7

Question 10 on its own page

Question 11

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 35

Question 11 on its own page

Question 12

+2 marksNumerical answer

Consider the following 2D data points along with its labels:

$x$	$y$
$\begin{bmatrix} 1 & 1 \end{bmatrix}^T$	1
$\begin{bmatrix} 1 & -1 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & 1 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & 2 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & -2 \end{bmatrix}^T$	0
$\begin{bmatrix} 3 & -3 \end{bmatrix}^T$	0
$\begin{bmatrix} 4 & -1 \end{bmatrix}^T$	1

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 1

Question 12 on its own page

Question 13

+3 marksNumerical answer

Consider the following 2D data points along with its labels:

$x$	$y$
$\begin{bmatrix} 1 & 1 \end{bmatrix}^T$	1
$\begin{bmatrix} 1 & -1 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & 1 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & 2 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & -2 \end{bmatrix}^T$	0
$\begin{bmatrix} 3 & -3 \end{bmatrix}^T$	0
$\begin{bmatrix} 4 & -1 \end{bmatrix}^T$	1

Based on the above data, answer the given subquestions.

Compute the Leave-one-out cross validation (LOOCV) error for the 3- nearest neighbour (3-NN) algorithm on this dataset. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.43 (accepted within ±0.02)

Question 13 on its own page

Question 14

+2 marksOne correct option

Consider the following 2D data points along with its labels:

$x$	$y$
$\begin{bmatrix} 1 & 1 \end{bmatrix}^T$	1
$\begin{bmatrix} 1 & -1 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & 1 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & 2 \end{bmatrix}^T$	1
$\begin{bmatrix} 2 & -2 \end{bmatrix}^T$	0
$\begin{bmatrix} 3 & -3 \end{bmatrix}^T$	0
$\begin{bmatrix} 4 & -1 \end{bmatrix}^T$	1

Based on the above data, answer the given subquestions.

Is it possible to reduce the cross-validation error obtained in the previous question by changing the label of certain points?

A
Yes
B
No
C
Cannot conclude from the given information.

Show answer

Correct answer

A
Yes

Question 14 on its own page