 NAME
 VERSION
 SYNOPSIS
 DESCRIPTION
 METHODS
 ATTRIBUTES
 THEORY
 SEE ALSO
 BASED ON
 AUTHORS
 COPYRIGHT AND LICENSE
NAME
AI::NaiveBayes  A Bayesian classifier
VERSION
version 0.03
SYNOPSIS
# AI::NaiveBayes objects are created by AI::NaiveBayes::Learner
# but for quick start you can use the 'train' class method
# that is a shortcut using default AI::NaiveBayes::Learner settings
my $classifier = AI::NaiveBayes>train(
{
attributes => {
sheep => 1, very => 1, valuable => 1, farming => 1
},
labels => ['farming']
},
{
attributes => {
vampires => 1, cannot => 1, see => 1, their => 1,
images => 1, mirrors => 1
},
labels => ['vampire']
},
);
# Classify a feature vector
my $result = $classifier>classify({bar => 3, blurp => 2});
# $result is now a AI::NaiveBayes::Classification object
my $best_category = $result>best_category;
DESCRIPTION
This module implements the classic "Naive Bayes" machine learning algorithm. This is a low level class that accepts only precomputed featurevectors as input, see AI::Classifier::Text for a text classifier that uses this class.
Creation of AI::NaiveBayes
classifier object out of training data is done by AI::NaiveBayes::Learner. For quick start you can use the limited train
class method that trains the classifier in a default way.
The classifier object is immutable.
It is a wellstudied probabilistic algorithm often used in automatic text categorization. Compared to other algorithms (kNN, SVM, Decision Trees), it's pretty fast and reasonably competitive in the quality of its results.
A paper by Fabrizio Sebastiani provides a really good introduction to text categorization: http://faure.iei.pi.cnr.it/~fabrizio/Publications/ACMCS02.pdf
METHODS
 new( model => $model )

Internal. See AI::NaiveBayes::Learner to learn how to create a
AI::NaiveBayes
classifier from training data.  train( LIST of HASHREFS )

Shortcut for creating a trained classifier using AI::NaiveBayes::Learner default settings. Arguments are passed to the
add_example
method of the AI::NaiveBayes::Learner object one by one.  classify( HASHREF )

Classifies a featurevector of the form:
{ feature1 => weight1, feature2 => weight2, ... }
The result is a
AI::NaiveBayes::Classification
object.  rescale

Internal
ATTRIBUTES
 model

Internal
THEORY
Bayes' Theorem is a way of inverting a conditional probability. It states:
P(yx) P(x)
P(xy) = 
P(y)
The notation P(xy)
means "the probability of x
given y
." See also "/mathforum.org/dr.math/problems/battisfore.03.22.99.html"" in "http: for a simple but complete example of Bayes' Theorem.
In this case, we want to know the probability of a given category given a certain string of words in a document, so we have:
P(words  cat) P(cat)
P(cat  words) = 
P(words)
We have applied Bayes' Theorem because P(cat  words)
is a difficult quantity to compute directly, but P(words  cat)
and P(cat)
are accessible (see below).
The greater the expression above, the greater the probability that the given document belongs to the given category. So we want to find the maximum value. We write this as
P(words  cat) P(cat)
Best category = ArgMax 
cat in cats P(words)
Since P(words)
doesn't change over the range of categories, we can get rid of it. That's good, because we didn't want to have to compute these values anyway. So our new formula is:
Best category = ArgMax P(words  cat) P(cat)
cat in cats
Finally, we note that if w1, w2, ... wn
are the words in the document, then this expression is equivalent to:
Best category = ArgMax P(w1cat)*P(w2cat)*...*P(wncat)*P(cat)
cat in cats
That's the formula I use in my document categorization code. The last step is the only nonrigorous one in the derivation, and this is the "naive" part of the Naive Bayes technique. It assumes that the probability of each word appearing in a document is unaffected by the presence or absence of each other word in the document. We assume this even though we know this isn't true: for example, the word "iodized" is far more likely to appear in a document that contains the word "salt" than it is to appear in a document that contains the word "subroutine". Luckily, as it turns out, making this assumption even when it isn't true may have little effect on our results, as the following paper by Pedro Domingos argues: "/www.cs.washington.edu/homes/pedrod/mlj97.ps.gz"" in "http:
SEE ALSO
Algorithm::NaiveBayes (3), AI::Classifier::Text(3)
BASED ON
Much of the code and description is from Algorithm::NaiveBayes.
AUTHORS
Zbigniew Lukasiak <zlukasiak@opera.com>
Tadeusz Sośnierz <tsosnierz@opera.com>
Ken Williams <ken@mathforum.org>
COPYRIGHT AND LICENSE
This software is copyright (c) 2012 by Opera Software ASA.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.