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

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Question: 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

Option 1: 'Features are equally important.' This is a vague statement. Naive Bayes does not explicitly assign equal importance to all features in the model; rather, it makes a strong independence assumption and uses the likelihoods of each feature given the class. In practice, some features may contribute more or less to distinguishing classes, depending on their conditional distributions and the data. The phrasing could be interpreted as incorrect if interpreted as a modeling assumption, but it is not the core defining incorrectness of Naive Bayes.

Option 2: 'Features are statistically dependent of one another given the class value.' This is the opposite of a central Naive Bayes assumption. Naive Bayes assumes conditional independence of features given the class label, meaning features are treated as independent when the class is fixed. Therefore, asserting dependence given the class value contradicts the foundational assumption of Naive Bayes and is the likely incorrect statement among the options.

Option 3: 'The model calculates the posterior probability of each class given the input features.' This is accurate. Naive Bayes computes the posterior P(C|X) for each class C by combining the prior P(C) with the likelihoods P(X|C) under the independence assumption, typically via Bayes’ theorem.

Option 4: 'Features can be nominal or numeric.' This is also correct in the usual Naive Bayes implementations. Naive Bayes can handle both discrete (nominal) features, with appropriate likelihoods (e.g., categorical distributions), and continuous features, often modeled with Gaussian, Poisson, or other distributions depending on the variant.

Why this option is identified as incorrect hinges on the core modelling assumption. If we accept the standard Naive Bayes framework, the claim that features are statistically dependent given the class contradicts the independence assumption, making it the incorrect statement among the four.

To summarize the incorrect option rationale: the incorrect statement is the one that asserts dependence among features conditioned on the class, because Naive Bayes relies on conditional independence to factorize the joint likelihood into a product of individual feature likelihoods. The other statements align with common interpretations or capabilities of Naive Bayes, namely computing posteriors, accommodating nominal or numeric features, and the nuanced point about feature importance which can be context-dependent but does not define the core incorrectness in this set.

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