Data Science from Scratch by Grus Joel

Author:Grus, Joel
Language: eng
Format: epub
Publisher: O'Reilly Media
Published: 2015-04-14T04:00:00+00:00

For example, if 50% of spam messages have the word viagra, but only 1% of nonspam messages do, then the probability that any given viagra-containing email is spam is:

A More Sophisticated Spam Filter

Imagine now that we have a vocabulary of many words . To move this into the realm of probability theory, we’ll write for the event “a message contains the word .” Also imagine that (through some unspecified-at-this-point process) we’ve come up with an estimate for the probability that a spam message contains the ith word, and a similar estimate for the probability that a nonspam message contains the ith word.

The key to Naive Bayes is making the (big) assumption that the presences (or absences) of each word are independent of one another, conditional on a message being spam or not. Intuitively, this assumption means that knowing whether a certain spam message contains the word “viagra” gives you no information about whether that same message contains the word “rolex.” In math terms, this means that:

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