Question1Question 1 Copy of SE Q1 Which of the following models can NOT achieve training error of zero on any linearly separable dataset? (you can choose more than one option) Perceptron Hard-margin SVM 15-NN Decision tree Reset多项选择题
A
Perceptron
B
Hard-margin SVM
C
15-NN
D
Decision tree

Question

Question1Question 1 Copy of SE Q1 Which of the following models can NOT achieve training error of zero on any linearly separable dataset? (you can choose more than one option) Perceptron Hard-margin SVM 15-NN Decision tree Reset多项选择题

A

Perceptron

B

Hard-margin SVM

C

15-NN

D

Decision tree

BlackTom AI · Accepted Answer

Consider the question: Which models can NOT guarantee zero training error on any linearly separable dataset? (multiple answers allowed)
Options: Perceptron, Hard-margin SVM, 15-NN, Decision tree

Option 1: Perceptron. In linearly separable data, the perceptron algorithm is guaranteed to converge to a weight vector that classifies the training data correctly, thus achieving zero training error after sufficient updates. Therefore, this option is not correct as a model that cannot achieve zero training error.

Option 2: Hard-margin SVM. For linearly separable data, the hard-margin SVM finds a separating hyperplane with maximum margin and correctly classifies all training examples, yielding zero training error. Hence, this option does not represent a model that cannot achieve zero training error.

Option 3: 15-NN. K-Nearest Neighbors with k = 15 does not come with a guarantee of zero training error. Even on linearly separable datasets, the 15-NN classifier may, for some training points, predict the opposite label if the majority among the 15 nearest neighbors belongs to the other class, especially when excluding the point itself or due to local class distribution. In other words, zero training error is not guaranteed for all linearly separable datasets with this instance-based method.

Option 4: Decision tree. A decision tree with sufficient depth can perfectly memorize and separate the training examples, including those that are linearly separable, leading to zero training error on the training set. Therefore, this option does not represent a model that cannot achieve zero training error.

Summary. Among the provided options, only 15-NN lacks a guaranteed zero-training-error property on every linearly separable dataset, while the others can achieve zero training error given appropriate training conditions or model capacity.

Question1Question 1 Copy of SE Q1 Which of the following models can NOT achieve training error of zero on any linearly separable dataset? (you can choose more than one option) Perceptron Hard-margin SVM 15-NN Decision tree Reset多项选择题

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