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IIT M FOUNDATION AN EXAM QDF3 16 Mar - 16 Mar 2025

MLT Quiz 214 questions40 marks6 MCQ · 6 SA · 2 MSQFoundation / afternoon / QDF3

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Q1MCQ3 marks

Q2MCQ3 marks

Q3MCQ2 marks

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

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

Q4MCQ2 marks

To prevent numerical errors when calculating the variance of Gaussianfeatures.
To ensure that unseen categorical feature values receive small but nonzeroprobabilities.
To strengthen the model’s predictions by increasing the weight of certainfeatures.
To balance the likelihood values of all features before computing posteriorprobabilities.

Q5MCQ4 marks

(a)
(b)
Insufficient information

Q6MSQ3 marksselect all that apply

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

Q7MSQ3 marksselect all that apply

Q8SA4 marks

Your numeric answer:

Q9SA4 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

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

Q10SA3 marks

Your numeric answer:

Q11SA2 marks

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

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.

Your numeric answer:

Q14MCQ2 marks

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

Yes
No
Cannot conclude from the given information.

Answer key

Q1 (MCQ, 3 marks): C
Q2 (MCQ, 3 marks): B
Q3 (MCQ, 2 marks): D
Q4 (MCQ, 2 marks): B
Q5 (MCQ, 4 marks): A
Q6 (MSQ, 3 marks): B, C
Q7 (MSQ, 3 marks): A, C
Q8 (SA, 4 marks): 483
Q9 (SA, 4 marks): 1
Q10 (SA, 3 marks): 7
Q11 (SA, 2 marks): 35
Q12 (SA, 2 marks): 1
Q13 (SA, 3 marks): 0.41 to 0.45
Q14 (MCQ, 2 marks): A

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. Ridge Regression

Concept: Ridge regression is a regularized version of linear regression that includes a penalty term to prevent overfitting.
Optimization Problem:

\min_{w \in \mathbb{R}^n} \sum_{i=1}^{n} (w^T x_i - y_i)^2 \quad \text{subject to} \quad \|w\|^2 \leq \theta

Key Idea: Ridge regression shrinks the coefficients to reduce variance.
Equation:

\|\hat{w}_R\| \leq \|\hat{w}\|

where $\hat{w}_R$ is the ridge coefficient estimate and $\hat{w}$ is the least squares estimate.

2. Naive Bayes Classifier

Concept: Naive Bayes is a probabilistic classifier based on Bayes' theorem with strong independence assumptions between features.
Number of Parameters: For $k$ classes and $n$ binary features, the number of parameters is:

(k - 1) + k \cdot n

Laplace Smoothing: Adds a small constant to feature counts to avoid zero probabilities.

P(x_i|y) = \frac{N_{x_i|y} + 1}{N_y + V}

where $N_{x_i|y}$ is the count of feature $x_i$ in class $y$ , $N_y$ is the total count of features in class $y$ , and $V$ is the number of possible feature values.

3. Decision Trees

Impurity Measures: Gini impurity and entropy are used to measure the disorder in a node.
Information Gain: Used to decide the best split.

\text{Information Gain} = \text{Entropy}(D) - \gamma \text{Entropy}(D_{Yes}) - (1 - \gamma) \text{Entropy}(D_{No})

Key Idea: The impurity is maximum when $p = 0.5$ for binary classification.

4. Kernel Regression

Concept: Kernel regression uses a kernel function to compute similarity between data points in a transformed feature space.
Polynomial Kernel:

K(x, x') = (x^T x' + 1)^d

Role of Kernel: Captures non-linear relationships by mapping data to a higher-dimensional space.

5. Gradient Descent

Concept: An optimization algorithm used to minimize the loss function.
Update Rule:

w = w - \eta \nabla f(w)

where $\eta$ is the learning rate and $\nabla f(w)$ is the gradient of the loss function.

6. k-Nearest Neighbors (k-NN)

Concept: A non-parametric method used for classification and regression.
Prediction: For a test point, the label is determined by the majority vote of its $k$ nearest neighbors.
Leave-One-Out Cross Validation (LOOCV): A method to evaluate the model's performance by leaving one data point out as the test set and using the rest as the training set.