The term "Naive" in Naive Bayes refers to the assumption of conditional independence among the features given the class label. In other words, it assumes that the presence or absence of a particular feature is unrelated to the presence or absence of any other feature, given the class variable.
Mathematically, for a given class variable C and a dependent feature vector X = (x1, x2, ..., xn), the Naive Bayes classifier assumes that:
P(X|C) = P(x1|C) * P(x2|C) * ... * P(xn|C)
This assumption simplifies the computation of the likelihood term P(X|C) in Bayes' Theorem, as it allows the joint probability of the features given the class to be calculated as the product of the individual conditional probabilities.
However, in reality, the features may not always be conditionally independent. The assumption of conditional independence is a simplification that makes the Naive Bayes classifier computationally efficient and easier to implement. Despite this "naive" assumption, Naive Bayes often performs surprisingly well in practice, especially when the features are indeed conditionally independent or when the dependencies among features are not strong.
It's important to note that the term "Naive" does not imply that the classifier is unsophisticated or inferior. It simply refers to the simplifying assumption made about the independence of features. Naive Bayes can still be a powerful and effective classifier in many real-world applications, particularly in text classification, spam filtering, and sentiment analysis, where the assumption of conditional independence often holds reasonably well.