Question8 Which of the following statements is/are INCORRECT? (you can choose more than one) The decision boundary in a decision trees with depth one is always linear The decision boundary in K-nearest neighbours is generally not linear The decision boundary in Logistic regression is always linear in the feature space. The decision boundary in Naïve Bayes is always linear in the feature space. ResetMaximum marks: 1.5 Flag question undefined

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BlackTom AI · Accepted Answer

The question asks which statements are INCORRECT, and multiple selections may be possible. Here are the options analyzed one by one with reasoning that highlights why each is correct or incorrect.

Option 1: "The decision boundary in a decision trees with depth one is always linear". A depth-1 decision tree splits data based on a single feature threshold (or a simple condition) which results in a boundary that is axis-aligned and piecewise constant. In a 2D space this boundary is a straight line (a linear boundary) in the feature space, so this statement is consistent with how a depth-1 tree behaves. It is not wrong.

Option 2: "The decision boundary in K-nearest neighbours is generally not linear". KNN creates decision boundaries based on the local neighborhood of the training instances. As a result, the boundary can be highly nonlinear, reflecting the distribution of the training points in the feature space. This statement aligns with the typical behavior of KNN and is correct.

Option 3: "The decision boundary in Logistic regression is always linear in the feature space." Logistic regression models the log-odds as a linear combination of features, leading to a decision boundary that is linear in the feature space (i.e., a straight line in 2D, a hyperplane in higher dimensions). This is a defining property of logistic regression, so this statement is correct.

Option 4: "The decision boundary in Naïve Bayes is always linear in the feature space." Naive Bayes assumes conditional independence among features given the class and uses probability distributions to model P(feature|class). Depending on the distributions chosen (e.g., Gaussian, discrete), the resulting decision boundary can be nonlinear in the feature space. Therefore the blanket claim that the boundary is always linear is false, making this statement incorrect.

In summary, options 2 and 3 describe correct behaviors of the respective models, option 1 describes correct behavior for a depth-1 tree, and option 4 makes an overgeneralization about Naïve Bayes boundaries being always linear, which is not true. The key misconception in option 4 is assuming linearity for all Naïve Bayes configurations, whereas the boundary shape depends on the underlying feature distributions and can be nonlinear.

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