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IIT M DIPLOMA AN3 EXAM QPD3 29 Oct 2023 - 29 Oct 2023

MLF Quiz 115 questions40 marks7 MCQ · 5 SA · 3 MSQDiploma / QPD3

Elapsed 00:00

Q1MSQ2 marksselect all that apply

Which of the following is/are supervised learning task(s)?

Predicting future weather conditions based on the past weather observations.
Reducing the dimensionality of images while retaining essential features,enabling efficient storage and transmission.
Identifying objects in images with multiple categories, such as cats, dogs, cars,and trees.
Categorizing news articles into topics like politics, sports, entertainment, andtechnology.

Q2MCQ2 marks

Consider the following input data points: question figure

Consider the following input data points: Which among the following models has the least misclassification error?

Sign(x1 − 2)
Sign(x2 + 2)
Sign(x1 + x2)
Sign(x2 − x1)

Q3MCQ2 marks

Q4MCQ2 marks

Q5SA3 marks

Your numeric answer:

Q6SA3 marks

Your numeric answer:

Q7SA3 marks

Your numeric answer:

Q8SA3 marks

Your numeric answer:

Q9MSQ3 marksselect all that apply

f is discontinuous at x = 0.
f is differentiable.
f is not differentiable at x = 0.
f'(0) = 0

Q10MCQ3 marks

Q11MCQ3 marks

Q12MCQ3 marks

Q13MSQ4 marksselect all that apply

Select the correct options from the following.

Comprehension passage - the questions below it refer to this

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

Q14MCQ3 marks

Find the projection of b onto U.

Q15SA1 mark

Find the length of the error vector e =b − p, where p is the projection of b onto U. Enter the answer correct to two decimal places.

Your numeric answer:

Answer key

Q1 (MSQ, 2 marks): A, C, D
Q2 (MCQ, 2 marks): D
Q3 (MCQ, 2 marks): A
Q4 (MCQ, 2 marks): D
Q5 (SA, 3 marks): 0.25
Q6 (SA, 3 marks): 0.25
Q7 (SA, 3 marks): 4.88 to 4.95
Q8 (SA, 3 marks): 22
Q9 (MSQ, 3 marks): B, D
Q10 (MCQ, 3 marks): D
Q11 (MCQ, 3 marks): A
Q12 (MCQ, 3 marks): C
Q13 (MSQ, 4 marks): C, D
Q14 (MCQ, 3 marks): B
Q15 (SA, 1 marks): 3.70 to 3.78

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. Supervised Learning

Concepts: Predicting future weather conditions, identifying objects in images, categorizing news articles.
Key Points: Supervised learning involves labeled data and tasks like classification and regression.

2. Misclassification Error

Concepts: Evaluating models based on misclassification error.
Key Points: Different models can be compared based on their misclassification errors.

3. Column Space

Concepts: Determining if a vector belongs to the column space of a matrix.
Equations:

v = \begin{bmatrix} 2 \\ 1 \\ -2 \end{bmatrix}, \quad A = \begin{bmatrix} -8 & -2 & -9 \\ 6 & 4 & 8 \\ 4 & 0 & 4 \end{bmatrix}

4. Diagonalization of Matrices

Concepts: Finding a matrix $P$ such that $P^{-1}AP$ is diagonal.
Equations:

A = \begin{bmatrix} 8 & 3 \\ 2 & 7 \end{bmatrix}, \quad P = \begin{bmatrix} 3 & 1 \\ 2 & 1 \end{bmatrix}

5. Mean Squared Loss

Concepts: Calculating the mean squared loss for a regression model.
Equations:

h(x_1, x_2) = \frac{x_1 + x_2}{2}

\text{Mean Squared Loss} = \frac{1}{n} \sum_{i=1}^{n} (y_i - h(x_{1i}, x_{2i}))^2

6. Quadratic Curve Fitting

Concepts: Fitting a quadratic curve to given points and conditions.
Equations:

y = ax^2 + bx + c

y = -x

7. Directional Derivatives

Concepts: Calculating the derivative of a function in a specific direction.
Equations:

\nabla f \cdot \mathbf{u}

where $\mathbf{u}$ is the unit vector in the direction of interest.

8. Eigenvalues and Eigenvectors

Concepts: Using eigenvalues and eigenvectors to find properties of a matrix.
Equations:

A v_1 = \lambda_1 v_1, \quad A v_2 = \lambda_2 v_2

v_1 = [1, 1]^T, \quad v_2 = [1, 2]^T, \quad \lambda_1 = 2, \quad \lambda_2 = 3

9. Differentiability and Continuity

Concepts: Analyzing the differentiability and continuity of piecewise functions.
Equations:

f(x) = \begin{cases} e^{-1/x^2}, & x > 0 \\ 0, & x \leq 0 \end{cases}

10. Second Order Approximation

Concepts: Finding the second order approximation of a function.
Equations:

f(x, y) = e^{2y - x}

f(x, y) \approx 1 - x + 2y - 2xy + 2y^2 + \frac{x^2}{2}

11. Least Squares Method

Concepts: Finding the best fit line using the least squares method.
Equations:

\hat{y} = 0.7x - 1

12. Positive Definite and Semi-Definite Matrices

Concepts: Properties of symmetric matrices and their eigenvalues.
Key Points: Symmetric matrices with positive eigenvalues are positive definite; non-negative eigenvalues indicate positive semi-definiteness.

13. Eigenvalues and Diagonalizability

Concepts: Properties of eigenvalues and diagonalizability of matrices.
Key Points: Matrices can have complex eigenvalues and may not be diagonalizable if they have repeated eigenvalues.

14. Row Space and Null Space

Concepts: Understanding the row space and null space of matrices.
Key Points: Specific vectors can belong to the row space or null space of a matrix.

15. Projection onto Subspaces

Concepts: Projecting vectors onto subspaces.
Equations:

U = \text{span} \left\{ \begin{bmatrix} 1 \\ 1 \\ 2 \end{bmatrix}, \begin{bmatrix} 1 \\ -1 \\ 1 \end{bmatrix} \right\}, \quad b = \begin{bmatrix} 2 \\ 0 \\ -4 \end{bmatrix}