GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 13

Question

A decision tree classifier learned from a fixed training set achieves $100 \%$ accuracy. Which of the following models trained using the same training set will also achieve $100 \%$ accuracy?

i) Logistic regressor.
ii) A polynomial of degree one kernel $\text{SVM}$.
iii) A linear discriminant function.
iv) Naïve Bayes classifier.

• A. $\text{i}$
• B. $\text{i and ii}$
• C. all of the above
• D. none of the above

Answer 1

Most probably The Answer should be D) none of the above,

because decision tree can work with binary and mix means multi class classifier as well as binary,

so in the first two options, both are not capable of multi class, so the option is more towards D

Comments

But multiple binary classifiers can act as multi class classifier, right?

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Here the question is about whether in a fixed training set, will any other models get 100 % accuracy as decision tree? The answer should be No, because only decision tree has that capability to learn accurately from training set with 100 % accuracy , while any other models does this, though this kind of accuracy from training set leads to overfitting, so we should do pre-pruning before the tree goes deep and complex. 

No, Multi class Classifier is a non-binary classifier but it follows The same way as binary classifier, takes each class label with highest confidence respect to the remaining  class labels to classify each class labels.

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I agree with the reason you provided why only decision trees can get 100% accuracy on a fixed training set.

But what I’m saying is, multiple binary classifiers can act as a multi class classifier with One vs Rest and One vs One strategy.

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No, There is some slightly confusion to your understanding ! It’s a method ! Multi class classifier is a method ( boundary ) which uses similar strategy like method (boundary) Binary classifier to classify / separate each class,  but dissimilar to binary classifier ( as yudhistar, you are asking if multiple binary classifier can act as multi class classifier) , assume n classes are there., because here the class (1) is predicted (positive) against rest(n-1) classes (negative) and considered to be highest confidence against the rests to classify that class, so the approach is clear binary but can we say “multiple binary classifier”? as we are comparing one against the rest not between two class (binary) ! I hope you understood.

Answer 2

It is Option C(all of the above). If we can achieve 100% accuracy with decision tree classifier it means there is a clear boundary between two classes i.e two classes are well separated. Logistic as well as polynomial kernel with degree one and linear discriminant can easily identify the boundary.

Comments

Yes you are correct!

Answer 3

Option D is correct 

From following figure we can say that 

Logistic regression can never classify XOR data 100% accurately but decision tree can. ( LR classify data linearly), SVM can Classify this data by projecting into higher dimension, 

Also i found from online mock test platform that LDA doesn’t mentioned in option ( Replaced it by KNN)

Since, option i is not true there is only one correct option is left which is Option D, None of the above or Naive Bayes Classifier

 

Answer 4

a decision tree can learn an XOR data but logistic and naive bayes can't
Classification algorithms like Logistic Regression and Naive Bayes only work on linearly separable problems
Considering XOR,

Logistic Regression and Naive Bayes can't classify it
Decision tree, KNN and SVM with polyn kernal can.