The correct answer is B) attributes are statistically dependent of one another given the class value, and I will explain in detail why this statement is incorrect and why the other options (A) attributes are equally important and (C) attributes are statistically independent of one another given the class value are not necessarily correct either.

B) The incorrect statement:

Attributes are statistically dependent on one another given the class value is not true in the context of Naive Bayes classification. In fact, Naive Bayes relies on the assumption of attribute independence given the class value, which is why it is called “Naive.”

This assumption simplifies the calculations and makes the algorithm computationally efficient, but it might not always hold true in real-world scenarios.

Now, let’s examine each of the options in detail:

A) Attributes are equally important:

In Naive Bayes, attributes are not assumed to be equally important. The algorithm assigns probabilities to each attribute based on the training data and their relationship with the class variable.

The importance of each attribute is determined by its contribution to the likelihood of a particular class. While Naive Bayes assumes independence among attributes, it does not assume that attributes are equally important. Some attributes may have a stronger influence on the classification decision than others.

C) Attributes are statistically independent of one another given the class value:

This statement is partially correct. Naive Bayes does assume that attributes are statistically independent of one another given the class value. In other words, it assumes that the presence or absence of one attribute does not affect the presence or absence of another attribute once the class value is known.

However, this assumption might not always hold in practice. In some real-world scenarios, attributes may exhibit some degree of statistical dependence, and the “naive” independence assumption may not be entirely accurate. Despite this simplification, Naive Bayes can perform surprisingly well in a wide range of classification tasks.

In Naive Bayes classification, the algorithm calculates the probability of a particular class given a set of attributes. This is done using Bayes’ theorem and the independence assumption among attributes.

The algorithm calculates the likelihood of each attribute given the class, the prior probability of the class, and the evidence (the joint probability of the attributes). The class with the highest posterior probability is chosen as the predicted class.

While the assumption of attribute independence simplifies the calculations, it is a “naive” assumption and may not hold true in every real-world scenario. In practice, Naive Bayes can work well when the independence assumption is approximately met, or when the inter-attribute dependencies are not strong enough to significantly impact the classification results.

In summary, the statement that attributes are statistically dependent on one another given the class value is incorrect for Naive Bayes classification. The algorithm assumes attribute independence given the class value, making it a simple and efficient classification method.

However, the other options should be clarified: attributes are not assumed to be equally important, and Naive Bayes does assume attribute independence, even though it’s a simplifying assumption that may not always hold perfectly in practice.