# What does these points mean in Naive Bayes?

I have two concept related questions related to Naïve Bayes.

Naïve Bayes is robust to irrelevant features. What does this mean? Can anyone give an example how does the irrelevant features cancels out and what are the irrelevant features?

It is optimal if the independence assumption holds. Can anyone give an example of independence assumption not holding? I think it would be related to presence of words like Hong Kong, United Kingdom etc in a sentence.

Regards, Akshit Bhatia

• Ask the decision tree question separately, it's not related to NB Feb 1, 2020 at 14:12

Imagine a classifier for sentiment analysis. For a strongly positive word like $$w=great$$, the conditional probability $$p(w|pos)$$ is going to be quite high whereas $$p(w|neg)$$ is going to be quite low, so the posterior $$p(pos|d)$$ for a document $$d$$ containing this word is likely to be much higher than $$p(neg|d)$$.
Now what happens with a neutral word $$w=today$$? Neither $$p(w|pos)$$ or $$p(w|neg)$$ is going to be much higher than the other. So all other things being equal, the difference between the two posterior probabilities is not going to depend much on this word compared to other more relevant words, for instance "great".