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GATE 2024 DA Q.18: solution and answer

GATE 2024 · DAQ.18 · 1 mark · MCQ

Match the items in Column 1 with the items in Column 2 in the following table:

| Column 1 | Column 2 |
|---|---|
| (p) Principal Component Analysis | (i) Discriminative Model |
| (q) Naïve Bayes Classification | (ii) Dimensionality Reduction |
| (r) Logistic Regression | (iii) Generative Model |

GATE 2024 DA question 18: A two-column table.Tap to open full size
Figure from the GATE 2024 DA paper. It is part of the question.
Figure description

A two-column table. Column 1 rows: (p) Principal Component Analysis, (q) Naïve Bayes Classification, (r) Logistic Regression. Column 2 rows: (i) Discriminative Model, (ii) Dimensionality Reduction, (iii) Generative Model.

  1. (A)

    (p) − (iii), (q) − (i), (r) − (ii)

  2. (B)

    (p) − (ii), (q) − (i), (r) − (iii)

  3. (C)

    (p) − (ii), (q) − (iii), (r) − (i)

  4. (D)

    (p) − (iii), (q) − (ii), (r) − (i)

Answer and solution

ANSWER

Option (C): (p) - (ii), (q) - (iii), (r) - (i).

Official answer: CSource: Official answer key, GATE 2024 DA (IISc Bengaluru)

  1. Principal Component Analysis projects the data onto the directions of largest variance, which are the top eigenvectors of the covariance matrix. It reduces the number of features, so it is a dimensionality-reduction method: (p) - (ii).

  2. Naive Bayes models how the data arise. It estimates the class prior and the class-conditional likelihood , assuming the features are conditionally independent given the class. It then applies Bayes' theorem to get . Because it models the joint distribution , it is a generative model: (q) - (iii).

  3. Logistic regression models the posterior directly, , and never models . Modelling the conditional distribution directly makes it a discriminative model: (r) - (i).

  4. The matching is (p)-(ii), (q)-(iii), (r)-(i). This is option (C).

KEY IDEA

A generative model learns the joint distribution , usually as (Naive Bayes). A discriminative model learns directly (logistic regression). PCA is unsupervised and has no class model, so it is dimensionality reduction.

WATCH OUT FOR

Swapping Naive Bayes and logistic regression because both are called classifiers that output class probabilities. What separates them is whether is modelled (generative) or only (discriminative). Another slip is labelling PCA a generative model.

From the GATE 2024 DA paper. Every question of this paper · Download the full paper · All 4 Logistic, k-NN, naive Bayes questions, with notes

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