We recently came up with three proofs that taken together suggest that the naive independence assumptions made in the Naive Bayes classifier are quite unnecessary for achieving the accuracy it is capable of.
A new classifier based on this math (called the Perplexed Bayes Classifier) is described in our recent research paper.
This blog post is to announce that we’ve also provided a mathematics companion to the paper.
The mathematics companion may be downloaded from: http://www.aiaioo.com/publications/icon2015_mathematics_companion.pdf
What is the Perplexed Bayes Classifier?
The perplexed bayes classifier is a classifier that resembles the naive bayes classifier but does not suffer from one of the shortcomings of the naive bayes classifier (a tendency to be unjustifiably overconfident about its predictions).
The following diagram shows how the reliability curves of the perplexed bayes classifier look alongside the naive bayes classifier’s.