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IIT M FOUNDATION AN3 EXAM QPF3 16 JULY 2023 - 16 Jul 2023

MLT Quiz 113 questions50 marks6 SA · 5 MSQ · 2 MCQFoundation / QPF3

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Q1MCQ4 marks

Q2MCQ4 marks

Q3MSQ4 marksselect all that apply

Select all true statements regarding standard PCA applied on a centered dataset.

The variance of the dataset along the first principal component is maximum.
The variance of the dataset along the first principal component is minimum.
The first principal component is the unit norm eigenvector corresponding tothe largest eigenvalue of the covariance matrix.
The first principal component is the unit norm eigenvector corresponding tothe smallest eigenvalue of the covariance matrix.

Q4MSQ4 marksselect all that apply

The covariance matrix corresponding to this dataset has 30 non-zeroeigenvalues.
The covariance matrix corresponding to this dataset has only four non-zeroeigenvalues.
The residues will become zero after four rounds
By utilizing four principal component vectors and their correspondingcoefficients, we have the ability to reconstruct the complete dataset using representatives.

Q5MSQ5 marksselect all that apply

Which of the following statements about kernel PCA is/are always true?

Q6MSQ5 marksselect all that apply

Q7MSQ3.5 marksselect all that apply

Which of the following statements is/are true?

Q8SA4 marks

Your numeric answer:

Q9SA4 marks

Your numeric answer:

Q10SA4 marks

Your numeric answer:

Q11SA4.5 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

What is the value of a? Enter your answer correct to three decimal places.

Your numeric answer:

Q13SA2 marks

What is the value of b? Enter your answer correct to two decimal places.

Your numeric answer:

Answer key

Q1 (MCQ, 4 marks): C
Q2 (MCQ, 4 marks): C
Q3 (MSQ, 4 marks): A, C
Q4 (MSQ, 4 marks): B, C, D
Q5 (MSQ, 5 marks): B, C
Q6 (MSQ, 5 marks): A, B, D
Q7 (MSQ, 3.5 marks): A, C
Q8 (SA, 4 marks): 60
Q9 (SA, 4 marks): 70
Q10 (SA, 4 marks): 40
Q11 (SA, 4.5 marks): 0.15 to 0.35
Q12 (SA, 2 marks): 1.25 to 1.5
Q13 (SA, 2 marks): 0.25 to 0.55

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 Functions and Transformation Mapping

Kernel Functions: Functions that compute the dot product of the transformed input data in a higher-dimensional space.
Transformation Mapping ( $\phi$ ): Maps input data to a higher-dimensional space.
Example: Given a kernel function $k([x_1, x_2]^T, [y_1, y_2]^T)$ , find the appropriate $\phi$ that transforms the data.

2. K-means Clustering

Algorithm: Iterative algorithm to partition data into $k$ clusters.
Euclidean Distance: Metric used to calculate the distance between data points and centroids.
Termination: Algorithm terminates when centroids do not change significantly between iterations.
Example: Given four points and initial centroids, determine the number of iterations and final centroids.

3. Principal Component Analysis (PCA)

Variance Maximization: PCA finds the directions of maximum variance in the data.
Eigenvectors and Eigenvalues: Principal components are the eigenvectors of the covariance matrix, corresponding to the largest eigenvalues.
Reconstruction: Data can be reconstructed using the principal components and their coefficients.
Example: Statements about variance, eigenvalues, and reconstruction in PCA.

4. Kernel PCA

Non-linear PCA: Extends PCA to non-linear data using kernel functions.
Valid Kernels: Conditions for valid kernel functions and their combinations.
Example: Statements about the number of principal components and valid kernel functions.

5. Bernoulli Distribution and Maximum Likelihood Estimation (MLE)

Bernoulli Distribution: Models binary data.
MLE: Method to estimate the parameters of a statistical model.
Example: Given MLE estimate for $p$ , find the number of zeros in a dataset.

6. Beta Distribution and Bayesian Inference

Beta Distribution: Prior and posterior distributions for the parameter $p$ in a Bernoulli model.
Bayesian Inference: Updating the prior distribution based on observed data.
Example: Given prior and posterior Beta distributions, find the number of zeros in a dataset.

7. Gaussian Mixture Models (GMM)

GMM: Probabilistic model that assumes data is generated from a mixture of Gaussian distributions.
Probability Calculation: Calculate the probability that a data point belongs to a specific component.
Example: Given GMM parameters, find the probability that a point comes from the first component.

8. Coordinate Transformation in PCA

Principal Components: Directions in the data that capture the most variance.
Projection: Transforming data points into the coordinate system formed by the principal components.
Example: Given principal components and a data point, find its representation in the new coordinate system.