da5003_2025T3_ET_FN.pdf

Algorithms for Data Science · End Term · Sep 2025 FN

Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

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.

Question 3 MSQ · 3.0 marks

Consider a dataset [[IMAGE:5e221a58d8075f44_2_2]] of [[IMAGE:5e221a58d8075f44_2_3]] data-points in [[IMAGE:5e221a58d8075f44_2_4]] . Given [[IMAGE:5e221a58d8075f44_2_5]] , let [[IMAGE:5e221a58d8075f44_2_6]] be a linear map from [[IMAGE:5e221a58d8075f44_2_7]] , an approximate isometry as guaranteed by the JL lemma. Which of the following are true?

[[IMAGE:5e221a58d8075f44_2_8]]
[[IMAGE:5e221a58d8075f44_2_9]] , for all [[IMAGE:5e221a58d8075f44_2_10]]
[[IMAGE:5e221a58d8075f44_2_11]] , for all [[IMAGE:5e221a58d8075f44_2_12]]
[[IMAGE:5e221a58d8075f44_2_13]] , for all [[IMAGE:5e221a58d8075f44_2_14]]

A published solution is not available for this question yet.

Question 4 MSQ · 2.0 marks

A family of hash functions [[IMAGE:5e221a58d8075f44_3_15]] is called [[IMAGE:5e221a58d8075f44_3_16]] -sensitive for some [[IMAGE:5e221a58d8075f44_3_17]] , [[IMAGE:5e221a58d8075f44_3_18]] , [[IMAGE:5e221a58d8075f44_3_19]] if exactly two conditions hold for any pair of points [[IMAGE:5e221a58d8075f44_3_20]] . What are these two conditions?

[[IMAGE:5e221a58d8075f44_3_21]]
[[IMAGE:5e221a58d8075f44_3_22]]
[[IMAGE:5e221a58d8075f44_3_23]]
[[IMAGE:5e221a58d8075f44_3_24]]

A published solution is not available for this question yet.

Question 5 MSQ · 3.0 marks

Let [[IMAGE:5e221a58d8075f44_3_25]] be an undirected, weighted graph, with non-negative edge weights. [[IMAGE:5e221a58d8075f44_3_26]] is the [[IMAGE:5e221a58d8075f44_3_28]] matrix of weights. [[IMAGE:5e221a58d8075f44_3_27]] is a diagonal matrix such that . Also, [[IMAGE:5e221a58d8075f44_3_29]] is the Laplacian of the graph. Which of the following are true?

[[IMAGE:5e221a58d8075f44_3_30]]
[[IMAGE:5e221a58d8075f44_3_31]]
[[IMAGE:5e221a58d8075f44_3_32]] is an eigenvalue of [[IMAGE:5e221a58d8075f44_3_33]]
[[IMAGE:5e221a58d8075f44_3_34]] is a positive definite matrix

A published solution is not available for this question yet.

Question 6 NAT · 2.0 marks

Let [[IMAGE:5e221a58d8075f44_4_35]] be a matrix whose non-zero singular values are [[IMAGE:5e221a58d8075f44_4_36]] and [[IMAGE:5e221a58d8075f44_4_37]] . If [[IMAGE:5e221a58d8075f44_4_38]] is the best rank-3 approximation of [[IMAGE:5e221a58d8075f44_4_39]] , then compute [[IMAGE:5e221a58d8075f44_4_40]] .

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 [[IMAGE:5e221a58d8075f44_4_41]] . Given a set of [[IMAGE:5e221a58d8075f44_4_42]] distinct points in [[IMAGE:5e221a58d8075f44_4_43]] , what is the maximum number of labelings possible using classifiers from [[IMAGE:5e221a58d8075f44_4_44]] , the class of interval classifiers?

A published solution is not available for this question yet.

Question 8 NAT · 3.0 marks

Let [[IMAGE:5e221a58d8075f44_4_45]] be the set of all axis-parallel cuboids in [[IMAGE:5e221a58d8075f44_4_46]] , a generalization of the axis-parallel rectangles in [[IMAGE:5e221a58d8075f44_4_47]] to three dimensions. Find the VC dimension of [[IMAGE:5e221a58d8075f44_4_48]] .

A published solution is not available for this question yet.

Question 9 NAT · 2.0 marks

[[IMAGE:5e221a58d8075f44_5_49]]

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 [[IMAGE:5e221a58d8075f44_5_50]] . What is [[IMAGE:5e221a58d8075f44_5_51]] ?

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 [[IMAGE:5e221a58d8075f44_6_52]] with [[IMAGE:5e221a58d8075f44_6_53]] . Let the intermediate random vector generated by the mechanism be [[IMAGE:5e221a58d8075f44_6_54]] . What is the probability of observing the intermediate bit pattern [[IMAGE:5e221a58d8075f44_6_55]] ? That is, compute [[IMAGE:5e221a58d8075f44_6_56]] . Enter your answer correct to three decimal places.

A published solution is not available for this question yet.

Question 12 NAT · 3.0 marks

[[IMAGE:5e221a58d8075f44_6_57]]

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 [[IMAGE:5e221a58d8075f44_7_58]] , where a triangle classifier is one that predicts [[IMAGE:5e221a58d8075f44_7_59]] for all points inside the triangle and [[IMAGE:5e221a58d8075f44_7_60]] 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 [[IMAGE:5e221a58d8075f44_8_61]] is the joint distribution over the features and labels and [[IMAGE:5e221a58d8075f44_8_62]] is a finite hypothesis class. [[IMAGE:5e221a58d8075f44_8_63]] is a dataset of [[IMAGE:5e221a58d8075f44_8_64]] points randomly sampled in an i.i.d manner from [[IMAGE:5e221a58d8075f44_8_65]] . [[IMAGE:5e221a58d8075f44_8_66]] is some classifier output by an algorithm given [[IMAGE:5e221a58d8075f44_8_67]] as input. [[IMAGE:5e221a58d8075f44_8_68]] is some small positive real number. Let [[IMAGE:5e221a58d8075f44_8_69]] and [[IMAGE:5e221a58d8075f44_8_70]] be two events defined as follows: [[IMAGE:5e221a58d8075f44_8_71]] Based on the above data, answer the given subquestions.

What is [[IMAGE:5e221a58d8075f44_8_72]] ?

Generalization error
Estimation error
Approximation error
Bayes error

A published solution is not available for this question yet.

Question 15 MCQ · 2.0 marks

Which of the following is true?

[[IMAGE:5e221a58d8075f44_8_73]]
[[IMAGE:5e221a58d8075f44_8_74]]
[[IMAGE:5e221a58d8075f44_8_75]]

A published solution is not available for this question yet.

Question 16 MSQ · 2.0 marks

Uniform convergence results show that [[IMAGE:5e221a58d8075f44_9_76]] whenever [[IMAGE:5e221a58d8075f44_9_77]] , where [[IMAGE:5e221a58d8075f44_9_78]] is some small positive real number. Which of the following is/are true?

If [[IMAGE:5e221a58d8075f44_9_79]] decreases, [[IMAGE:5e221a58d8075f44_9_80]] increases.
If [[IMAGE:5e221a58d8075f44_9_81]] increases, then [[IMAGE:5e221a58d8075f44_9_82]] increases.
If [[IMAGE:5e221a58d8075f44_9_83]] increases, [[IMAGE:5e221a58d8075f44_9_84]] increases.
[[IMAGE:5e221a58d8075f44_9_85]] is independent of [[IMAGE:5e221a58d8075f44_9_86]] .

A published solution is not available for this question yet.

Question 17 NAT · 2.0 marks

[[IMAGE:5e221a58d8075f44_10_87]] Based on the above data, answer the given subquestions.

Find the absolute value of the estimation error for [[IMAGE:5e221a58d8075f44_10_88]] . Enter the answer correct to three decimal places.

A published solution is not available for this question yet.

Question 18 NAT · 2.0 marks

[[IMAGE:5e221a58d8075f44_10_87]] 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

[[IMAGE:5e221a58d8075f44_12_89]] Based on the above data, answer the given subquestions.

[[IMAGE:5e221a58d8075f44_12_90]]

A published solution is not available for this question yet.

Question 20 NAT · 2.0 marks

[[IMAGE:5e221a58d8075f44_12_89]] Based on the above data, answer the given subquestions.

[[IMAGE:5e221a58d8075f44_13_91]]

A published solution is not available for this question yet.