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IIT M FOUNDATION AN EXAM QDF2 03 Aug - 03 Aug 2025

MLT Quiz 215 questions40 marks7 MCQ · 6 SA · 2 MSQFoundation / afternoon / QDF2

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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:

\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 finding the mode of the posterior distribution.
Equation:

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

\lambda = \gamma^2

3. Linear Regression

Concept: Linear regression models the relationship between a dependent variable and one or more independent variables using a linear approach.
Equation:

y = w^T x + \epsilon

\min_{w \in \mathbb{R}^d} ||X^T w - y||_2^2

4. Model Evaluation

Concept: Evaluating the performance of a model using metrics like training error and validation error.
Principle: Choose hyperparameters based on the lowest validation error and a relatively low training error.

5. Generative and Discriminative Models

Concept: Generative models learn the joint probability distribution $P(x, y)$ , while discriminative models learn the conditional probability distribution $P(y|x)$ .
Principle: Generative models are interested in how the features are generated, while discriminative models focus on modeling $P(y|x)$ .

6. Decision Trees

Concept: Decision trees are a non-parametric supervised learning method used for classification and regression.
Principle: Decision trees split the data based on features to create branches that lead to a decision.
Equation: Entropy and Information Gain

H(S) = -p_+ \log_2(p_+) - p_- \log_2(p_-)

IG(S, A) = H(S) - \sum_{v \in \text{Values}(A)} \frac{|S_v|}{|S|} H(S_v)

7. Naive Bayes Classifier

Concept: Naive Bayes is a probabilistic classifier based on applying Bayes' theorem with strong independence assumptions between the features.
Equation:

P(y|x) = \frac{P(y) P(x|y)}{P(x)}

8. k-Nearest Neighbors (k-NN)

Concept: k-NN is a non-parametric method used for classification and regression.
Principle: The output is determined by the majority class or the average of the k-nearest neighbors.