CSCE 470 Lecture 22

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No class friday.

Naïve Bayes' Classifier

Spam or not spam. That is the question.

From last time, we discussed assigning classes using naïve Bayes'

$c_{MAP}={\underset {c\in C}{\mathrm {argmax} }}\ P(c|d)=\mathrm {argmax} \ P(c)\,\prod P(t_{k}|c)$

Let's classify a new email. Based on what we know about $P(c)$ (90% of all emails are spam), this message is probably spam just without looking at it.

Let's look at the words in the document and factor their probabilities in.

Suppose a regular "spam" message has about 2000 words and a regular "not spam" message has 1000 words.

term	spam	not spam
"click"	100	10

$P(\mathrm {click} ~|~\mathrm {spam} )={\frac {100}{2000}}$

$P(\mathrm {click} ~|~\neg \mathrm {spam} )={\frac {10}{1000}}$

What if a word does not occur in the training data?

• ignore it
• give it a little number (smoothing)

Confusion Matrix

		It really is
		spam	not spam
I predict	spam	50	40
	not spam	3	7

Precision: 57 correct out of 100

Accuracy: (number of correct predictions out of number of predictions) = 50/90