Why is Naive Bayes called 'naive', and why does it still work?
It naively assumes that features are independent of each other once the class is known. That is rarely true, but classification only needs the correct class to have the highest score, so predictions are often good even when the probabilities are off.
Explain it simply
In a spam email, "lottery" and "winner" tend to appear together. Naive Bayes ignores this and treats each word as a separate piece of evidence, as if two witnesses had never spoken to each other. In reality they heard the same rumour, so counting both as independent over-counts the evidence.
Example
Without the assumption, the model needs P(word1, word2, ..., wordN | class), which requires astronomically many combinations to estimate. With it:
P(w1, w2, ..., wN | class) = P(w1|class) x P(w2|class) x ... x P(wN|class)Only N small numbers per class are needed, so it trains quickly even on 10,000 words.
Why it still works: if "lottery" and "winner" are double counted, spam gets over-scored, but a spam email is usually still scored above a ham email, so the ranking of classes stays correct.
What suffers: the predicted probabilities become over-confident, pushed close to 0 or 1. If you need trustworthy probabilities, calibrate them, for example with CalibratedClassifierCV.
When it fails: features that are strong duplicates, or where the interaction between features is the signal (as in XOR-type patterns).
What to say in the interview
"Naive refers to the conditional independence assumption between features given the class. It is almost always violated, but the classification can still be right because only the class ranking matters. The cost is over-confident probabilities, which I would calibrate if they are used for decisions."
Common mistakes
- Saying the features must be completely independent for the model to work at all.
- Trusting its probabilities as calibrated.