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# NAME

Math::KullbackLeibler::Discrete

version 0.07

# SYNOPSIS

This module computes Kullback-Leibler divergence for two discrete distributions, using smoothing.

``````    use Math::KullbackLeibler::Discrete;

my \$P = { a => 1/2, b => 1/4, c => 1/4 };
my \$Q = { a => 7/12, b => 2/12, d => 3/12 };

my \$kl = kl( \$P, \$Q );

# optionally set the smoothing epsilon
my \$kl2 = kl( \$P, \$Q, epsilon => 0.0001 );

# setting epsilon to 0 results in no smoothing.
my \$kl3 = kl( \$P, \$Q, epsilon => 0 );``````

# NAME

Math::KullbackLeibler::Discrete - Computes Kullback-Leibler divergence for two discrete distributes.

# EXPORT

## kl

Computes smoothed KL.

Receives two mandatory arguments: two anonymous hashrefs, that map events to their probabilities.

Implementation based on the description presented at http://www.cs.bgu.ac.il/~elhadad/nlp09/KL.html.

The smoothing amount can be specified as parameter:

``   kl( \$P, \$Q, epsilon => 0.001 );``

This makes it possible to turn of smoothing, defined epsilon as zero. However, notice that this will lead to errors in case of divergent domains.

# AUTHOR

Alberto Simoes, `<ambs at cpan.org>`

# BUGS

Please report any bugs or feature requests to `bug-math-kullbackleibler-discrete at rt.cpan.org`, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=Math-KullbackLeibler-Discrete. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

# SUPPORT

You can find documentation for this module with the perldoc command.

``    perldoc Math::KullbackLeibler::Discrete``

You can also look for information at:

# ACKNOWLEDGEMENTS

Thanks to Michael Elhadad for making his lecture on-line, so I found a nice and clean explanation of how this metric could be computed and implemented.

Copyright 2013 Alberto Simões.

This program is free software; you can redistribute it and/or modify it under the terms of the the Artistic License (2.0). You may obtain a copy of the full license at:

Any use, modification, and distribution of the Standard or Modified Versions is governed by this Artistic License. By using, modifying or distributing the Package, you accept this license. Do not use, modify, or distribute the Package, if you do not accept this license.

If your Modified Version has been derived from a Modified Version made by someone other than you, you are nevertheless required to ensure that your Modified Version complies with the requirements of this license.

This license does not grant you the right to use any trademark, service mark, tradename, or logo of the Copyright Holder.

This license includes the non-exclusive, worldwide, free-of-charge patent license to make, have made, use, offer to sell, sell, import and otherwise transfer the Package with respect to any patent claims licensable by the Copyright Holder that are necessarily infringed by the Package. If you institute patent litigation (including a cross-claim or counterclaim) against any party alleging that the Package constitutes direct or contributory patent infringement, then this Artistic License to you shall terminate on the date that such litigation is filed.

Disclaimer of Warranty: THE PACKAGE IS PROVIDED BY THE COPYRIGHT HOLDER AND CONTRIBUTORS "AS IS' AND WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES. THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR NON-INFRINGEMENT ARE DISCLAIMED TO THE EXTENT PERMITTED BY YOUR LOCAL LAW. UNLESS REQUIRED BY LAW, NO COPYRIGHT HOLDER OR CONTRIBUTOR WILL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING IN ANY WAY OUT OF THE USE OF THE PACKAGE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

# AUTHOR

Alberto Simões <ambs@cpan.org>