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IIT M IMPROVEMENT AN EXAM QIV2 03 Aug - 03 Aug 2025

MLT Quiz 215 questions40 marks7 MCQ · 6 SA · 2 MSQImprovement / afternoon / QIV2

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Q1MCQ4 marks

Q2MCQ3 marks

Q3MCQ3 marks

Setting 3, because it has the lowest training error, indicating the best fit to thetraining data.
Setting 2, because it has the lowest validation error and a relatively lowtraining error, indicating a good generalization.
Setting 1, because it has the highest number of iterations and therefore likelyto be more stable.
Setting 4, because it uses the highest learning rate and converges the fastest.

Q4MCQ3 marks

Q5MCQ2 marks

TRUE
FALSE

Q6MCQ1 mark

TRUE
FALSE

Q7MSQ2 marksselect all that apply

Q8MSQ2 marksselect all that apply

Which among the following are true?

Q9SA3 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

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

Q10MCQ3 marks

Which among the following represents the correct decision boundary for the decision tree? Note: Here + represents the label 1 and − represents the label 0.

Q11SA2 marks

What will be the prediction for the new datapoint (2, 2)?

Your numeric answer:

Comprehension passage - the questions below it refer to this

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

Q12SA2 marks

Your numeric answer:

Q13SA3 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

Suppose you want to build a decision tree to help diagnose a certain disease based on patient data. You have a dataset of 1000 patients labeled as either “positive” or “negative”. Here, positive represents patients with the disease and negative represents no disease. One of the feature used to diagnose is headache. Below is the breakdown of the patients reporting headache: Headache present: 300 positive, 50 negative Headache not present: 100 positive, 550 negative question figure

Q14SA3 marks

What is the entropy of the root node? Enter the answer correct to two decimal places.

Your numeric answer:

Q15SA4 marks

What is the information gain for choosing the feature “headache” for splitting at the root node? Enter the answer correct to two decimal places.

Your numeric answer:

Answer key

Q1 (MCQ, 4 marks): A
Q2 (MCQ, 3 marks): C
Q3 (MCQ, 3 marks): B
Q4 (MCQ, 3 marks): C
Q5 (MCQ, 2 marks): A
Q6 (MCQ, 1 marks): A
Q7 (MSQ, 2 marks): A, C
Q8 (MSQ, 2 marks): A, C
Q9 (SA, 3 marks): 4.2
Q10 (MCQ, 3 marks): B
Q11 (SA, 2 marks): 0
Q12 (SA, 2 marks): 0.22 to 0.26
Q13 (SA, 3 marks): 1
Q14 (SA, 3 marks): 0.95 to 0.99
Q15 (SA, 4 marks): 0.34 to 0.38

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. Maximum Likelihood Estimation (MLE)

Concept: MLE is a method of estimating the parameters of a statistical model by maximizing the likelihood function.
Equation: For a given model $y_i | x_i \sim N(\log(wx_i), 1)$ , the MLE estimate $\hat{w}_{MLE}$ is given by:

\hat{w}_{MLE} = \exp \left( \frac{1}{n} \sum_{i=1}^{n} (y_i - \log(x_i)) \right)

2. Maximum A Posteriori (MAP) Estimation

Concept: MAP estimation is a Bayesian approach to estimate parameters by maximizing the posterior distribution.
Equation: For a linear regression model with Gaussian priors, the MAP estimator $\hat{w}_{\text{MAP}}$ is given by:

\hat{w}_{\text{MAP}} = \arg \min_{w} \left\{ \|y - X^T w\|^2 + \lambda \|w\|^2 \right\}

where $\lambda = \frac{\sigma^2}{\gamma^2}$ .

3. Linear Regression and Sum of Squared Errors

Concept: Linear regression models the relationship between a dependent variable and one or more independent variables. The sum of squared errors is minimized to find the best-fit line.
Equation: The sum of squared errors is given by:

\| y - X^T w \|_2^2

Maximizing the conditional log-likelihood of $w$ is equivalent to minimizing the sum of squared errors.

4. Projection in Linear Regression

Concept: In linear regression, $X^T w^*$ is the projection of the labels onto the subspace spanned by the features.
Equation: The solution $w^*$ lies in the span of the data points.

5. Generative and Discriminative Models

Concept: Generative models focus on how the data was generated, while discriminative models focus on modeling the conditional probability $p(y|x)$ .
Examples: Gaussian Naive Bayes is a generative model.

6. k-Nearest Neighbors (k-NN) Regression

Concept: k-NN is a non-parametric method used for classification and regression. For regression, it predicts the value based on the average of the k-nearest neighbors.
Example: For a 3-NN regressor, the predicted value for a test point is the average of the 3 closest training points.

7. Decision Trees

Concept: Decision trees are used for classification and regression. They split the data based on features to make predictions.
Example: A decision tree for binary classification with features $f_1$ and $f_2$ .

8. Naive Bayes Classifier

Concept: Naive Bayes is a probabilistic classifier based on Bayes' theorem with an assumption of independence between features.
Equation: For a binary feature $f_1$ and a Gaussian feature $f_2$ , the probability of a test point $x_{test}$ given a label is calculated using the product of the individual probabilities.

9. Entropy and Information Gain

Concept: Entropy measures the impurity or disorder in a dataset. Information gain measures the reduction in entropy achieved by partitioning the data based on a feature.
Equation: Entropy $H$ is given by:

H = - \sum p(x) \log_2 p(x)

Information gain $IG$ is given by:

IG = H_{\text{parent}} - \sum \frac{N_{\text{child}}}{N_{\text{parent}}} H_{\text{child}}