Math::KullbackLeibler::Discrete

NAME

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

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 );

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 Simões,

BUGS

Please report any bugs or feature requests on https://github.com/ambs/Math-KullbackLeibler-Discrete/issues

SUPPORT

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

• perldoc Math::KullbackLeibler::Discrete

You can also look for information at:

• RT: CPAN's request tracker (report bugs here)

  http://rt.cpan.org/NoAuth/Bugs.html?Dist=Math-KullbackLeibler-Discrete

• AnnoCPAN: Annotated CPAN documentation

  http://annocpan.org/dist/Math-KullbackLeibler-Discrete

• CPAN Ratings

  http://cpanratings.perl.org/d/Math-KullbackLeibler-Discrete

• Search CPAN

  http://search.cpan.org/dist/Math-KullbackLeibler-Discrete/

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.

LICENSE AND COPYRIGHT

Copyright 2013-2014 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:

http://www.perlfoundation.org/artistic_license_2_0

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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.

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