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IIT M DIPLOMA AN EXAM QDD3 01 Dec 2024 - 01 Dec 2024

MLT Quiz 215 questions50 marks8 SA · 5 MCQ · 2 MSQDiploma / afternoon / QDD3

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Comprehension passage - the questions below it refer to this

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

Q1MCQ3 marks

Q2SA4 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

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

Q3SA4 marks

Your numeric answer:

Q4SA3 marks

Your numeric answer:

Q5SA4 marks

Your numeric answer:

Q6SA4 marks

Your numeric answer:

Q7SA4 marks

Suppose you want to use a Naive Bayes classifier to predict whether a student will pass or fail an exam based on two features: the number of hours they studied and whether they attended review sessions. Assume that the features are conditionally independent given the exam outcome and that the variances of the study hours distributions are equal for both pass and fail categories. How many parameters are required to classify a new student using this Naive Bayes classifier?

Your numeric answer:

Q8MSQ4 marksselect all that apply

Select all true statements.

Comprehension passage - the questions below it refer to this

Consider a binary classification problem with a training dataset of 100 points, evenly distributed between two classes (50 points in each class). You decide to train a k-NN algorithm with k = 3. Each point is considered its own neighbor during classification. Based on the above data, answer the given subquestions.

Q9SA3 marks

What is the minimum number of misclassifications that can occur in the training dataset when using this k-NN algorithm?

Your numeric answer:

Q10MCQ2 marks

Assuming there are outliers, the decision boundary becomes smoother with decreasing value of k in a k-NN algorithm.

TRUE
FALSE

Comprehension passage - the questions below it refer to this

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

Q11MCQ2 marks

TRUE
FALSE

Q12MCQ4 marks

Comprehension passage - the questions below it refer to this

Consider a binary classification problem in which a decision tree is classifying data points into two classes, A and B. In a particular node of the tree, 60% of the data points belong to class A, while the remaining 40% belong to class B. Based on the above data, answer the given subquestions.

Q13MCQ2 marks

Do you have enough information to find the entropy of this node?

Q14SA4 marks

If the answer to the previous question is ”Yes,” calculate the entropy of this node to three decimal places. If the answer to the previous question is ”No,” enter -1 as your answer.

Your numeric answer:

Q15MSQ3 marksselect all that apply

Answer key

Q1 (MCQ, 3 marks): D
Q2 (SA, 4 marks): 2.31 to 2.35
Q3 (SA, 4 marks): 0.94 to 0.96
Q4 (SA, 3 marks): 0
Q5 (SA, 4 marks): 2
Q6 (SA, 4 marks): 0
Q7 (SA, 4 marks): 6
Q8 (MSQ, 4 marks): A, D, E
Q9 (SA, 3 marks): 0
Q10 (MCQ, 2 marks): B
Q11 (MCQ, 2 marks): A
Q12 (MCQ, 4 marks): C
Q13 (MCQ, 2 marks): A
Q14 (SA, 4 marks): 0.94 to 1.01
Q15 (MSQ, 3 marks): A, C

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. Kernel Regression and Polynomial Kernels

Kernel Regression: A non-parametric method to estimate the conditional expectation of a random variable.
Polynomial Kernel: $k(x_i, x_j) = (1 + x_i^T x_j)^2$
Kernel Matrix (K): Computed using the kernel function.
Weight Vector: $w = \phi(X)\alpha$ , where $\alpha = (K)^{-1}y$

2. Naïve Bayes Algorithm

Conditional Probability: $P(f_i = 1 \mid y = j)$
Complement Rule: $P(f_i = 0 \mid y = j) = 1 - P(f_i = 1 \mid y = j)$
Prediction: Based on the maximum posterior probability.

3. k-Nearest Neighbors (k-NN)

Distance Metric: Euclidean distance.
Prediction: Majority vote among the k-nearest neighbors.
Cross-Validation: Leave-one-out cross-validation for model evaluation.

4. Decision Trees

Information Gain: Measure of the effectiveness of a question in partitioning the dataset.
Entropy: Measure of impurity in a node.
Hyperparameters: Depth of the tree, chosen using cross-validation.

5. Linear Regression

Loss Function: $L(w) = \sum_{i=1}^{n} (w^T x_i - y_i)^2$
Optimal Weight Vector: $w^*$
Ridge Regression: Regularized linear regression with L2 penalty.
Bayesian Formulation: Prior distribution for weights, e.g., Laplace prior.

6. Model Evaluation

Mean Squared Error (MSE): Measure of the quality of an estimator.
Cross-Validation: Technique for assessing how the results of a statistical analysis will generalize to an independent dataset.

Equations

Kernel Regression

k(x_i, x_j) = (1 + x_i^T x_j)^2

K = \begin{bmatrix} k(x_1, x_1) & k(x_1, x_2) & \cdots & k(x_1, x_n) \\ k(x_2, x_1) & k(x_2, x_2) & \cdots & k(x_2, x_n) \\ \vdots & \vdots & \ddots & \vdots \\ k(x_n, x_1) & k(x_n, x_2) & \cdots & k(x_n, x_n) \end{bmatrix}

w = \phi(X)\alpha

\alpha = (K)^{-1}y

Naïve Bayes

P(f_i = 0 \mid y = j) = 1 - P(f_i = 1 \mid y = j)

P(y = j \mid f_1, f_2) \propto P(y = j) \prod_{i=1}^{2} P(f_i \mid y = j)

Linear Regression

L(w) = \sum_{i=1}^{n} (w^T x_i - y_i)^2

\hat{w}_{Ridge} = \arg \min_{w} \sum_{i=1}^{n} (w^T x_i - y_i)^2 + \lambda \|w\|_2^2

\hat{w}_{MAP} = \arg \min_{w} \sum_{i=1}^{n} (w^T x_i - y_i)^2 + \lambda \|w\|_1

Entropy

H = -\sum_{i} p_i \log_2 p_i

Graph 1: Machine Learning Techniques Overview

Graph 2: Kernel Regression

Graph 3: Naïve Bayes

Graph 4: Decision Trees

Graph 5: Linear Regression

These graphs and summaries should help you understand the core topics and their relationships for your exam preparation.