Which classifier is based on assuming independence among features and combines probabilities?

Which classifier is based on assuming independence among features and combines probabilities?

• A. Logistic Regression
• B. Naive Bayes Classifier
• C. K-Nearest Neighbors
• D. Decision Tree

Answer: (B)

The key idea tested here is using the independence of features to combine probabilities through Bayes’ rule. A Naive Bayes classifier treats each feature as conditionally independent of the others given the class, which lets us compute the likelihood of the observed features as a simple product of individual likelihoods: P(features | class) = ∏ P(feature_i | class). Then we combine that with the prior P(class) to get the posterior P(class | features) = P(class) × ∏ P(feature_i | class), up to a normalization factor. This multiplicative combination of probabilities across features is what makes Naive Bayes efficient, especially with many features. This approach is what sets it apart from the other methods. K-nearest neighbors makes decisions based on the labels of nearby instances and does not use probability products or an independence assumption. Decision trees split data to reduce impurity and don’t rely on multiplying likelihoods across features. Logistic regression models P(class | features) directly using a linear combination of features passed through a sigmoid, rather than combining feature likelihoods conditioned on the class. Even if the independence assumption isn’t perfectly true in practice, Naive Bayes often performs well because the wrong assumptions can cancel out or still capture useful signal, and the method remains robust and fast.

The key idea tested here is using the independence of features to combine probabilities through Bayes’ rule. A Naive Bayes classifier treats each feature as conditionally independent of the others given the class, which lets us compute the likelihood of the observed features as a simple product of individual likelihoods: P(features | class) = ∏ P(feature_i | class). Then we combine that with the prior P(class) to get the posterior P(class | features) = P(class) × ∏ P(feature_i | class), up to a normalization factor. This multiplicative combination of probabilities across features is what makes Naive Bayes efficient, especially with many features.

This approach is what sets it apart from the other methods. K-nearest neighbors makes decisions based on the labels of nearby instances and does not use probability products or an independence assumption. Decision trees split data to reduce impurity and don’t rely on multiplying likelihoods across features. Logistic regression models P(class | features) directly using a linear combination of features passed through a sigmoid, rather than combining feature likelihoods conditioned on the class.

Even if the independence assumption isn’t perfectly true in practice, Naive Bayes often performs well because the wrong assumptions can cancel out or still capture useful signal, and the method remains robust and fast.