Supervised Learning - Machine Learning - Data Science & Artificial Intelligence Previous Year Questions

1

2024 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2024

Consider the dataset with six datapoints: \( \{(\mathbf{x}_1, y_1), (\mathbf{x}_2, y_2), \ldots, (\mathbf{x}_6, y_6)\} \), where \( \mathbf{x}_1 = \begin{bmatrix} 1 \\ 0 \end{bmatrix} \), \( \mathbf{x}_2 = \begin{bmatrix} 0 \\ 1 \end{bmatrix} \), \( \mathbf{x}_3 = \begin{bmatrix} 0 \\ -1 \end{bmatrix} \), \( \mathbf{x}_4 = \begin{bmatrix} -1 \\ 0 \end{bmatrix} \), \( \mathbf{x}_5 = \begin{bmatrix} 2 \\ 2 \end{bmatrix} \), \( \mathbf{x}_6 = \begin{bmatrix} -2 \\ -2 \end{bmatrix} \), and the labels are given by \( y_1 = y_2 = y_5 = 1 \), and \( y_3 = y_4 = y_6 = -1 \). A hard margin linear support vector machine is trained on the above dataset.
Which ONE of the following sets is a possible set of support vectors?

A

\(\{\mathbf{x}_1, \mathbf{x}_2, \mathbf{x}_5\} \)

B

\(\{\mathbf{x}_3, \mathbf{x}_4, \mathbf{x}_5\} \)

C

\(\{\mathbf{x}_4, \mathbf{x}_5\} \)

D

\(\{\mathbf{x}_1, \mathbf{x}_2, \mathbf{x}_3, \mathbf{x}_4\} \)

Open complete paper

2

2024 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2024

Given a dataset with K binary-valued attributes (where K > 2) for a two-class classification task, the number of parameters to be estimated for learning a naive Bayes classifier is

A

\(2^K + 1\)

B

\(2K + 1\)

C

\(2^{K+1} + 1\)

D

\(K^2 + 1\)

Open complete paper

3

2024 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2024

For any binary classification dataset, let \(S_B \in \mathbb{R}^{d \times d}\) and \(S_W \in \mathbb{R}^{d \times d}\) be the between-class and within-class scatter (covariance) matrices, respectively. The Fisher linear discriminant is defined by \(u^* \in \mathbb{R}^d\) that maximizes \(J(u) = \frac{u^T S_B u}{u^T S_W u}\). If \(\lambda = J(u^*)\), \(S_W\) is non-singular and \(S_B \neq 0\), then \((u^*, \lambda)\) must satisfy which ONE of the following equations?
Note: \(\mathbb{R}\) denotes the set of real numbers.

A

\(S_W^{-1} S_B u^* = \lambda u^*\)

B

\(S_W u^* = \lambda S_B u^*\)

C

\(S_B S_W u^* = \lambda u^*\)

D

\(u^{*T} u^* = \lambda^2\)

Open complete paper

4

2024 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2024

Consider the following figures representing datasets consisting of two-dimensional features with two classes denoted by circles and squares.
Which of the following is/are TRUE?

A

(i) is linearly separable.

B

(ii) is linearly separable.

C

(iii) is linearly separable.

D

(iv) is linearly separable.

Check answer

Open complete paper

5

2024 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2024

Details of ten international cricket games between two teams “Green” and “Blue” are given in Table C. This table consists of matches played on different pitches, across formats along with their winners. The attribute Pitch can take one of two values: spin-friendly (represented as S) or pace-friendly (represented as F). The attribute Format can take one of two values: one day match (represented as O) or test match (represented as T).
A cricket organization would like to use the information given in Table C to develop a decision-tree model to predict outcomes of future games between these two teams.
To develop such a model, the computed InformationGain(C, Pitch) with respect to the Target is ______. (rounded off to two decimal places).
Table C

Match Number	Pitch	Format	Winner (Target)
1	S	T	Green
2	S	T	Blue
3	F	O	Blue
4	S	O	Blue
5	F	T	Green
6	F	O	Blue
7	S	O	Green
8	F	T	Blue
9	F	O	Blue
10	S	O	Green

Check answer

Open complete paper

6

2024 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2024

Given the two-dimensional dataset consisting of 5 data points from two classes (circles and squares) and assume that the Euclidean distance is used to measure the distance between two points. The minimum odd value of \(k\) in \(k\)-nearest neighbor algorithm for which the diamond (◇) shaped data point is assigned the label square is ______.

Check answer

Open complete paper

7

2025 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2025

Consider designing a linear classifier \[ y = \text{sign}(f(x; w, b)), \quad f(x; w, b) = w^\top x + b \] on a dataset \(D = \{(x_1, y_1), (x_2, y_2), \ldots, (x_N, y_N)\}\), \(x_i \in \mathbb{R}^d\), \(y_i \in \{+1, -1\}\), \(i = 1, 2, \ldots, N\). Recall that the sign function outputs +1 if the argument is positive, and -1 if the argument is non-positive. The parameters \(w\) and \(b\) are updated as per the following training algorithm: \[ w_{new} = w_{old} + y_n x_n, \quad b_{new} = b_{old} + y_n \] whenever \(\text{sign}(f(x_n; w_{old}, b_{old})) \ne y_n\). In other words, whenever the classifier wrongly predicts a sample \((x_n, y_n)\) from the dataset, \(w_{old}\) gets updated to \(w_{new}\) and likewise \(b_{old}\) gets updated to \(b_{new}\). Consider the case \((x_n, +1), f(x_n; w_{old}, b_{old}) < 0\). Then

A

\(f(x_n; w_{new}, b_{new}) > f(x_n; w_{old}, b_{old})\)

B

\(f(x_n; w_{new}, b_{new}) < f(x_n; w_{old}, b_{old})\)

C

\(f(x_n; w_{new}, b_{new}) = f(x_n; w_{old}, b_{old})\)

D

\(y_n f(x_n; w_{old}, b_{old}) > 1\)

Open complete paper

8

2025 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2025

Given data \(\{(-1, 1), (2, -5), (3, 5)\}\) of the form \((x_i, y_i)\), we fit a model \(y = wx\) using linear least-squares regression. The optimal value of \(w\) is ______________ (Round off to three decimal places)

Check answer

Open complete paper

9

2025 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2025

The naive Bayes classifier is used to solve a two-class classification problem with class-labels \(y_1, y_2\). Suppose the prior probabilities are \(P(y_1) = \frac{1}{3}\) and \(P(y_2) = \frac{2}{3}\). Assuming a discrete feature space with \[P(x|y_1) = \frac{3}{4} \text{ and } P(x|y_2) = \frac{1}{4},\] for a specific feature vector \(x\). The probability of misclassifying \(x\) is ______________ (Round off to two decimal places)

Check answer

Open complete paper

10

2025 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2025

Consider designing a linear binary classifier \(f(x) = \text{sign}(w^Tx + b)\), \(x \in \mathbb{R}^2\) on the following training data:

Class-1: \(\left\{ \begin{pmatrix} 2 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 2 \end{pmatrix}, \begin{pmatrix} 2 \\ 2 \end{pmatrix} \right\}\), Class-2: \(\left\{ \begin{pmatrix} 0 \\ 0 \end{pmatrix} \right\}\)

Hard-margin support vector machine (SVM) formulation is solved to obtain \(w\) and \(b\). Which of the following options is/are correct?

A

\(w = \begin{pmatrix} 4 \\ 4 \end{pmatrix}\) and \(b = 1\)

B

The number of support vectors is 3

C

The margin is \(\sqrt{2}\)

D

Training accuracy is 98%

Check answer

Open complete paper

11

2025 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science & Artificial Intelligence (DA) 2025

Consider a two-class problem in \(\mathbb{R}^d\) with class labels red and green. Let \(\mu_{red}\) and \(\mu_{green}\) be the means of the two classes. Given test sample \(x \in \mathbb{R}^d\), a classifier calculates the squared Euclidean distance (denoted by \(\|\cdot\|^2\)) between \(x\) and the means of the two classes and assigns the class label that the sample \(x\) is closest to. That is, the classifier computes \(f(x) = \|\mu_{red} - x\|^2 - \|\mu_{green} - x\|^2\) and assigns the label red to \(x\) if \(f(x) < 0\), and green otherwise. Which of the following statements is/are correct?

A

The sample \(x = 0\) is assigned the label green if \(\|\mu_{red}\| < \|\mu_{green}\|\)

B

\(f\) is a linear function of \(x\)

C

\(f(x) = w^T x + b\), where \(w\) and \(b\) are functions of \(\mu_{red}\) and \(\mu_{green}\)

D

\(f\) is a quadratic polynomial in \(x\)

Check answer

Open complete paper

12

2026 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science and Artificial Intelligence (DA) 2026

Consider that you are training a classifier for a 10-class classification problem. Each input is represented as a 512-dimensional vector. There are 1000 samples, out of which first 100 will be used for testing. Let Leave-One-Out-Cross-Validation (LOOCV) be used for selection of the classifier model before testing. Which of the following options is the correct number of validation splits that will be generated?

A

10

B

512

C

900

D

1000

Open complete paper

13

2026 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science and Artificial Intelligence (DA) 2026

Consider that for a supervised learning task, the objective function being minimized is $f_w(x) = wx$, where $x \in \mathbb{R}$ is the input and $w \in \mathbb{R}$ is the parameter. Stochastic Gradient Descent with learning rate of 0.10 is used for parameter updates. Suppose that at the end of iteration $t$, the value of $w$ becomes 10.00. Let $x = 10.00$ be the input for iteration $(t+1)$. The value of $w$ at the end of iteration $(t+1)$ is ________. (Rounded off to two decimal places)

Check answer

Open complete paper

14

2026 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science and Artificial Intelligence (DA) 2026

Which of the following statements is true for Ridge Regression?

A

The regularizer in the objective function of Ridge Regression is used to guard against scenarios where the model works well for the test data, but poorly for the training data.

B

The regularizer of Ridge Regression uses \(L_1\) norm.

C

Ridge Regression aims to reduce the number of parameters that have negative values.

D

The regularizer of Ridge Regression may increase the bias of the model, but it helps in reducing the variance in predictions.

Open complete paper

15

2026 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science and Artificial Intelligence (DA) 2026

Consider that 20 stories of Author X and 10 stories of Author Y were kept together without mentioning the names of the authors. A classifier was then asked to predict the author (X or Y) of each of these stories. Let, out of X’s stories, 6 were classified as that of Y. On the other hand, out of Y’s stories, 2 were classified as that of X.
Considering X and Y as two classes, which of the following statements is/are true?

A

Accuracy of the classifier is 11/15.

B

Precision of Class X is higher than the Precision of Class Y.

C

Recall of Class X is higher than the Recall of Class Y.

D

Accuracy of the classifier is 14/15.

Check answer

Open complete paper

16

2026 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science and Artificial Intelligence (DA) 2026

Consider that Linear Ridge Regression is being used to learn a prediction function \( y_{pred} = w^T x \), where \( w, x \in \mathbb{R}^2 \) and Mean Absolute Error (MAE) is used to measure the prediction error. A weight of 0.20 is associated with the regularizer.
At an intermediate step of the training process, assume that the parameter \( w = [-3.00, 4.00]^T \). In the next step, for the input \( x = [1.00, 2.00]^T \), the predicted value of \( y \) is noted. Let the relation between \( x = [x_1, x_2]^T \) and the true value of \( y \) be \( y_{true} = x_1 + x_2 \).
The value of the overall regularized loss function for this instance is ______.
(Rounded off to two decimal places)

Check answer

Open complete paper

17

2026 · Data Science & Artificial Intelligence · Machine Learning · Supervised Learning

Data Science and Artificial Intelligence (DA) 2026

Consider a fully-connected feed-forward multi-layer perceptron. It has 30 neurons in the input layer, followed by two hidden layers and an output layer. The first hidden layer has 4 neurons and the second hidden layer has 3 neurons. The output layer has only one neuron. Assume that no bias parameters are used.

The number of learnable parameters in the multi-layer perceptron is __________ . (Answer in integer)

Check answer

Open complete paper