Home / Past papers / MLT Quiz 1 / this paper

IIT M QUIZ 1 FOUNDATION DAD DIPLOMA QPE2 16 Oct 2022 - 16 Oct 2022

MLT Quiz 122 questions100 marks11 SA · 9 MCQ · 2 MSQFoundation / Diploma / QPE2

Elapsed 00:00

Q1MCQ0 marks

Q2MCQ6 marks

Q3MCQ6 marks

Q4MCQ6 marks

Q5MCQ6 marks

Q6MCQ5 marks

Q7MCQ5 marks

Q8MSQ4 marksselect all that apply

Q9SA5 marks

Your numeric answer:

Q10SA5 marks

Your numeric answer:

Q11SA5 marks

Your numeric answer:

Q12SA5 marks

Your numeric answer:

Q13SA7 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

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

Q14SA3 marks

what is the probability of the following points x2,x1 (in that order) being chosen as initial cluster centers?

Your numeric answer:

Q15SA3 marks

what is the probability of the following points x2,x3 (in that order) being chosen as initial cluster centers?

Your numeric answer:

Q16SA3 marks

what is the probability of the following points x2,x5 (in that order) being chosen as initial cluster centers?

Your numeric answer:

Comprehension passage - the questions below it refer to this

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

Q17MCQ3 marks

Is this dataset centered?

Q18MSQ4 marksselect all that apply

Q19SA5 marks

If standard PCA is performed on this dataset, what is the variance along the first principal component?

Your numeric answer:

Q20SA4 marks

If standard PCA is performed on this dataset, what is the variance along the second principal component?

Your numeric answer:

Comprehension passage - the questions below it refer to this

Q21MCQ5 marks

What is the log-likelihood of this dataset under this distribution?

Q22SA5 marks

Your numeric answer:

Answer key

Q1 (MCQ, 0 marks): A
Q2 (MCQ, 6 marks): D
Q3 (MCQ, 6 marks): B
Q4 (MCQ, 6 marks): D
Q5 (MCQ, 6 marks): B
Q6 (MCQ, 5 marks): A
Q7 (MCQ, 5 marks): C
Q8 (MSQ, 4 marks): A, C
Q9 (SA, 5 marks): 0.09 to 0.11
Q10 (SA, 5 marks): 6
Q11 (SA, 5 marks): 15
Q12 (SA, 5 marks): 0.29 to 0.31
Q13 (SA, 7 marks): 6
Q14 (SA, 3 marks): 0.03 to 0.04
Q15 (SA, 3 marks): 0.01 to 0.02
Q16 (SA, 3 marks): 0.06 to 0.07
Q17 (MCQ, 3 marks): A
Q18 (MSQ, 4 marks): A, B
Q19 (SA, 5 marks): 12.4 to 12.6
Q20 (SA, 4 marks): 0
Q21 (MCQ, 5 marks): C
Q22 (SA, 5 marks): 0.32 to 0.34

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 Methods and Kernel PCA

Kernel Function: A function $k$ that computes the inner product of the images of two data points in a higher-dimensional space.

k(x, y) = \langle \phi(x), \phi(y) \rangle

Polynomial Kernel: A common kernel function used in kernel PCA.

k(x, y) = (x^T y + c)^d

Kernel PCA: A method to perform PCA in a higher-dimensional space using kernel functions.

2. Principal Component Analysis (PCA)

Principal Components: The directions in which the data varies the most.
Variance along Principal Components: The variance of the data along the principal components.

\theta = \frac{\text{variance along the first principal component}}{\text{sum of variances along all principal components}}

Compression Ratio: The ratio of the size of the original dataset to the size of the reconstructed dataset.

\text{Compression Ratio} = \frac{\text{size of original dataset}}{\text{size of reconstructed dataset}}

3. K-Means Clustering

Lloyd’s Algorithm: An iterative algorithm for K-means clustering.
Cluster Initialization: The initial selection of cluster centers.
Objective Function: The sum of squared distances of data points to their nearest cluster center.

Obj = \sum_{i=1}^{n} \min_{\mu_j} \|x_i - \mu_j\|^2

K-Means++: An algorithm for choosing initial cluster centers to improve the performance of K-means.

4. Gaussian Mixture Models (GMM) and EM Algorithm

Gaussian Mixture Model: A probabilistic model that assumes the data is generated from a mixture of Gaussian distributions.
EM Algorithm: An iterative algorithm for finding maximum likelihood estimates of parameters in probabilistic models.
E-Step: Computes the posterior probabilities of the latent variables.

\lambda_k^i = P(z_i = k | x_i)

M-Step: Updates the parameters of the model based on the posterior probabilities.

\pi_k = \frac{1}{n} \sum_{i=1}^{n} \lambda_k^i

5. Probability and Statistics

Bernoulli Distribution: A discrete probability distribution with two possible outcomes.

P(x = 1) = p, \quad P(x = 0) = 1 - p

Beta Distribution: A family of continuous probability distributions defined on the interval [0, 1].

\text{Beta}(\alpha, \beta)

Maximum Likelihood Estimation (MLE): A method of estimating the parameters of a statistical model.

\mathcal{L}(\theta | x) = \prod_{i=1}^{n} f(x_i | \theta)

Log-Likelihood: The logarithm of the likelihood function.

\log \mathcal{L}(\theta | x) = \sum_{i=1}^{n} \log f(x_i | \theta)

6. Linear Algebra

Centering a Dataset: Subtracting the mean from each data point to center the data around the origin.
Variance and Covariance: Measures of the spread and relationship between variables.

\text{Var}(X) = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2

\text{Cov}(X, Y) = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu_X)(y_i - \mu_Y)