5) What will be the prediction of Naïve Bayes for thew following new example:

Secondhand = no, Genre = literature, Price = expensive

Question

5) What will be the prediction of Naïve Bayes for thew following new example:

Secondhand = no, Genre = literature, Price = expensive

BlackTom AI · Accepted Answer

Question restatement: The task asks for the Naïve Bayes prediction for a new example with features: Secondhand = no, Genre = literature, Price = expensive. The answer choices are: 1) Purchased=true 2) Purchased=false.

Option 1: Purchased=true. In Naïve Bayes, the predicted class is the one with the highest posterior probability given the features: P(Purchased|Secondhand=no, Genre=literature, Price=expensive) ∝ P(Purchased) × P(Secondhand=no|Purchased) × P(Genre=literature|Purchased) × P(Price=expensive|Purchased). If, given the trained model, this product is larger than the corresponding product for Purchased=false, the model will assign Purchased=true. This option is consistent with the standard goal of choosing the class with the maximum posterior, and it aligns with the provided answer indicating that the model favors Purchased=true for this feature combination.

Option 2: Purchased=false. The counter-argument is that Naïve Bayes weighs the prior with the likelihoods of each feature under the false class: P(Purchased=false) × P(Secondhand=no|Purchased=false) × P(Genre=literature|Purchased=false) × P(Price=expensive|Purchased=false). If, after multiplying these likelihoods by the prior, this product were larger than the Purchased=true product, the model would predict false. However, in this scenario, the stated answer implies that the false class does not have the higher posterior, so this option is not selected by the model.

Conceptual nuance: Naïve Bayes treats features as conditionally independent given the class, so it multiplies the individual feature likelihoods for each class. The decision hinges on which class yields the greater product with its prior. The specific feature values (Secondhand=no, Genre=literature, Price=expensive) interact through their likelihoods P(Secondhand=no|Purchased), P(Genre=literature|Purchased), and P(Price=expensive|Purchased). Since the question provides Purchased=true as the correct option, the intended interpretation is that the combination of features yields a higher posterior for Purchased=true under the trained model.

Why the other option is not chosen: If Purchased=false were correct, the product P(Purchased=false) × P(Secondhand=no|Purchased=false) × P(Genre=literature|Purchased=false) × P(Price=expensive|Purchased=false) would exceed the Purchased=true product. Since the answer indicates Purchased=true, we infer that either the prior or one or more feature likelihoods for Purchased=true dominate, making the true class more probable. Misconceptions to avoid: assuming independence invalidly without considering priors, or ignoring how a single high or low likelihood for one feature can swing the overall posterior, could lead to predicting the incorrect class.

Summary of reasoning style: The model compares the two posterior probabilities and selects the class with the larger value. The given answer reflects that, for this feature combination, Purchased=true yields a higher posterior than Purchased=false, given the learned priors and likelihoods.

COMP4318 COMP5318 (NE) Homework w4

5) What will be the prediction of Naïve Bayes for thew following new example: Secondhand = no, Genre = literature, Price = expensive

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