The IIT Madras BS Machine Learning Techniques (MLT) Quiz 1 paper sat on 15 Mar 2026, in the January 2026 term: 12 questions for 31 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
Consider a clustering problem with
data-points and two clusters
. As initialization, a subset of the dataset comprising the first fifty data-points, call this
, are assigned to cluster
and the remaining points, call this
Scenario-1 is possible, but scenario-2 is impossible.
Scenario-1 is impossible, but scenario-2 is possible.
Both scenarios are possible.
Both scenarios are impossible.
Correct answer
Both scenarios are impossible.
Consider a polynomial kernel of degree
on a feature space of dimension
. How many features will the transformed space have
Correct answer: 35
Consider the Gaussian kernel,
with
. Compute the value of
and enter your answer correct to two decimal places.
Correct answer: 0.37 (accepted within ±0.03)
Consider the following data-points in a clustering problem with five data-points and three clusters (k = 3):
K-means
is used to initialize the three means. The first mean is chosen to be
and the second mean to be
. Find the probability of choosing
Correct answer: 0.5
Consider a cube of edge-length
centered at the origin with its corners represented as
. These eight points make up a dataset
. Based on the above data, answer the given subquestions.
Find the covariance matrix
of the dataset. Enter the sum of all the entries of
as the answer.
Correct answer: 3
Consider a cube of edge-length
centered at the origin with its corners represented as
. These eight points make up a dataset
. Based on the above data, answer the given subquestions.
Let
be some unit vector. Find the variance of the dataset along the direction
.
Correct answer: 1
Standard PCA is performed on a centered dataset in
. The first three principal components are:
The first two principal components are retained and the third is discarded. The coordinate representation of the data-point
after projection onto the first two principal components is
. Based on the above data, answer the given subquestions.
Find
. Enter your answer correct to three decimal places.
Correct answer: 2.121 (accepted within ±0.05)
Standard PCA is performed on a centered dataset in
. The first three principal components are:
The first two principal components are retained and the third is discarded. The coordinate representation of the data-point
after projection onto the first two principal components is
. Based on the above data, answer the given subquestions.
Find
. Enter your answer correct to three decimal places.
Correct answer: 0.707 (accepted within ±0.05)
Answer true or false for the given subquestions.
If
and
are valid kernels, then
is also a valid kernel.
True
False
Correct answer
True
Answer true or false for the given subquestions.
If
A is a data-matrix of shape
A^T A
and
A A^T have the same eigenvectors.
True
False
Correct answer
False
Let
be i.i.d. observations from the mixture distribution
where
The observed data are
Assume that the initial estimate of the mixing parameter is
Consider the E-step of the EM algorithm. Introduce latent variables
such that
if
is generated from
. Compute the posterior responsibility
Correct answer: 2.77 (accepted within ±0.03)
Let
be i.i.d. observations from the mixture distribution
where
The observed data are
Assume that the initial estimate of the mixing parameter is
Using a Maximum A Posteriori (MAP) decision rule, a data point
is assigned to mixture 2 if the posterior responsibility
. Based on the values calculated in the E-step, which data point(s) are classified as belonging to Component 2?
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(A figure from the original paper is missing from the source site.)
(A figure from the original paper is missing from the source site.)
All four points
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Correct answer
(A figure from the original paper is missing from the source site.)
