# Naive Bayes

Assume x\_i is given conditionally independent.

![](https://443921002-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGHUhl6VYqrZm4Re77O%2F-LTKxy37hNQ68Ltk2sPK%2F-LTL-VvmwPjpVfQPhcQg%2FScreen%20Shot%202018-12-09%20at%206.45.55%20PM.png?alt=media\&token=33d716de-74df-47d4-ac84-dcdd57aadeeb)

And pick whichever class has the highest posterior probability.

> **Pros:**
>
> Require less training data than e.g. logistic regression.

> **ML applications that contains naive Bayesian:**
>
> &#x20;   \- Sentimental analysis in Facebook;
>
> &#x20;   \- Documentation categorization for Page Rank in Google
>
> &#x20;   \- Email spam filtering in Gmail

