Question 2 MCQ · 2.0 marks
Which of the following metrics is the ERM primarily designed to maximize by design?
Accuracy
F1 score
Precision
Log loss
A published solution is not available for this question yet.
Algorithms for Data Science · End Term · Sep 2025 · FN
Algorithms for Data Science · End Term · Sep 2025 FN
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Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.
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Question 3 MSQ · 3.0 marks
Consider a dataset
of
data-points in
. Given
, let
be a linear map from
, an approximate isometry as guaranteed by the JL lemma. Which of the following are
true?
, for all
, for all
, for all
A published solution is not available for this question yet.
Question 4 MSQ · 2.0 marks
A family of hash functions
is called
-sensitive for some
,
,
if exactly two conditions hold for any pair of points
. What are these
two conditions?
A published solution is not available for this question yet.
Question 5 MSQ · 3.0 marks
Let
be an undirected, weighted graph, with non-negative edge weights.
is the
matrix of weights.
is a diagonal matrix such that . Also,
is the Laplacian of the
graph. Which of the following are true?
is an eigenvalue of
is a positive definite matrix
A published solution is not available for this question yet.
Question 6 NAT · 2.0 marks
Let
be a matrix whose non-zero singular values are
and
. If
is the best
rank-3 approximation of
, then compute
.
A published solution is not available for this question yet.
Question 7 NAT · 2.0 marks
Consider a binary classification problem with a single feature in
. Given a set of
distinct points
in
, what is the maximum number of labelings possible using classifiers from
, the class of
interval classifiers?
A published solution is not available for this question yet.
Question 8 NAT · 3.0 marks
Let
be the set of all axis-parallel cuboids in
, a generalization of the axis-parallel rectangles in
to three dimensions. Find the VC dimension of
.
A published solution is not available for this question yet.
Question 9 NAT · 2.0 marks
A published solution is not available for this question yet.
Question 10 NAT · 1.0 marks
The hypothesis class of axis parallel rectangles has a sample compression scheme of size
. What
is
?
A published solution is not available for this question yet.
Question 11 NAT · 3.0 marks
In the context of data privacy, consider the randomized response mechanism applied to the true
data
with
. Let the intermediate random vector generated by the
mechanism be
. What is the probability of observing the intermediate bit pattern
?
That is, compute
. Enter your answer correct to three decimal places.
A published solution is not available for this question yet.
Question 12 NAT · 3.0 marks
A published solution is not available for this question yet.
Question 13 NAT · 0.0 marks
**BONUS Question (0 marks)**Find the VC dimension of the set of all triangle classifiers in
, where
a triangle classifier is one that predicts
for all points inside the triangle and
for points outside
it.
A published solution is not available for this question yet.
Question 14 MCQ · 2.0 marks
Consider a binary classification problem where
is the joint distribution over the features and
labels and
is a finite hypothesis class.
is a dataset of
points randomly sampled in an
i.i.d manner from
.
is some classifier output by an algorithm given
as input.
is some
small positive real number. Let
and
be two events defined as follows:
Based on the above data, answer the given subquestions.
What is
?
Generalization error
Estimation error
Approximation error
Bayes error
A published solution is not available for this question yet.
Question 15 MCQ · 2.0 marks
Consider a binary classification problem where
is the joint distribution over the features and
labels and
is a finite hypothesis class.
is a dataset of
points randomly sampled in an
i.i.d manner from
.
is some classifier output by an algorithm given
as input.
is some
small positive real number. Let
and
be two events defined as follows:
Based on the above data, answer the given subquestions.
Which of the following is true?
A published solution is not available for this question yet.
Question 16 MSQ · 2.0 marks
Consider a binary classification problem where
is the joint distribution over the features and
labels and
is a finite hypothesis class.
is a dataset of
points randomly sampled in an
i.i.d manner from
.
is some classifier output by an algorithm given
as input.
is some
small positive real number. Let
and
be two events defined as follows:
Based on the above data, answer the given subquestions.
Uniform convergence results show that
whenever
, where
is some small
positive real number. Which of the following is/are true?
If
decreases,
increases.
If
increases, then
increases.
If
increases,
increases.
is independent of
.
A published solution is not available for this question yet.
Question 17 NAT · 2.0 marks
Based on the above data, answer the given subquestions.
Find the absolute value of the estimation error for
. Enter the answer correct to three decimal
places.
A published solution is not available for this question yet.
Question 18 NAT · 2.0 marks
Based on the above data, answer the given subquestions.
Find the absolute value of the approximation error.
A published solution is not available for this question yet.
Question 19 NAT · 2.0 marks
Based on the above data, answer the given subquestions.
A published solution is not available for this question yet.
Question 20 NAT · 2.0 marks
Based on the above data, answer the given subquestions.
A published solution is not available for this question yet.