Which of the following statements about Naive Bayes is incorrect? 1. Features are equally important 2. Features are statistically dependent of one another given the class value 3. The model calculates the posterior probability of each class given the input features 4. Features can be nominal or numeric

Question

BlackTom AI · Accepted Answer

We are evaluating statements about Naive Bayes to identify which one is incorrect.

Option a: 'Statement 3 is incorrect' — This claim would be false because Naive Bayes does compute the posterior probability P(C|X) for each class, using Bayes' rule and the feature likelihoods. The model combines prior P(C) with the product of conditional likelihoods P(Xi|C) to form P(C|X). Therefore, Statement 3 is actually correct, not incorrect.

Option b: 'Statement 1 is incorrect' — The statement says features are equally important. In the standard Naive Bayes framework, the features are treated as conditionally independent given the class, and each feature contributes via its conditional likelihood to the overall product. While one could interpret 'equally important' in different ways, the canonical NB formulation does not assign differential importance to features beyond their likelihoods; it effectively multiplies their contributions. So depending on interpretation, this could be considered acceptable for a naïve assumption. In the usual teaching, this statement is often treated as correct (not the incorrect one).

Option c: 'Statement 4 is incorrect' — Naive Bayes can indeed handle both nominal (categorical) and numeric features, with appropriate modeling for each type (e.g., discrete distributions for categorical features and Gaussian or other distributions for numeric features). Thus, Statement 4 is correct, not incorrect.

Option d: 'Statement 2 is incorrect' — This is the core incorrect claim. Naive Bayes assumes conditional independence of features given the class, meaning the features are not statistically dependent on each other when the class label is known. Therefore, asserting that features are statistically dependent given the class contradicts the Naive Bayes assumption. This makes Statement 2 the incorrect one.

Putting the pieces together, only Statement 2 is incorrect, which aligns with the provided answer choice identifying 'd. Statement 2 is incorrect' as the incorrect statement.

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类似问题

Which statements about Naive Bayes are true? (Select all that apply.)

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