Text::NSP::Measures::2D::MI::tmi - Perl module that implements True Mutual Information.


Basic Usage

  use Text::NSP::Measures::2D::MI::tmi;

  my $npp = 60; my $n1p = 20; my $np1 = 20;  my $n11 = 10;

  $tmi_value = calculateStatistic( n11=>$n11,

  if( ($errorCode = getErrorCode()))
    print STDERR $errorCode." - ".getErrorMessage()."\n"";
    print getStatisticName."value for bigram is ".$tmi_value."\n"";


Assume that the frequency count data associated with a bigram <word1><word2> is stored in a 2x2 contingency table:

          word2   ~word2
  word1    n11      n12 | n1p
 ~word1    n21      n22 | n2p
           np1      np2   npp

where n11 is the number of times <word1><word2> occur together, and n12 is the number of times <word1> occurs with some word other than word2, and n1p is the number of times in total that word1 occurs as the first word in a bigram.

The expected values for the internal cells are calculated by taking the product of their associated marginals and dividing by the sample size, for example:

          np1 * n1p
   m11=   ---------

True Mutual Information (tmi) is defined as the weighted average of the pointwise mutual informations for all the observed and expected value pairs.

 tmi = [n11/npp * log(n11/m11) + n12/npp * log(n12/m12) +
        n21/npp * log(n21/m21) + n22/npp * log(n22/m22)]

 PMI =   log (n11/m11)


calculateStatistic() - This method calculates the tmi value

INPUT PARAMS : $count_values .. Reference of an hash containing the count values computed by the program.

RETURN VALUES : $tmi .. TMI value for this bigram.

getStatisticName() - Returns the name of this statistic


RETURN VALUES : $name .. Name of the measure.


Ted Pedersen, University of Minnesota Duluth <>

Satanjeev Banerjee, Carnegie Mellon University <>

Amruta Purandare, University of Pittsburgh <>

Bridget Thomson-McInnes, University of Minnesota Twin Cities <>

Saiyam Kohli, University of Minnesota Duluth <>


Last updated: $Id:,v 1.22 2006/06/21 11:10:53 saiyam_kohli Exp $



                author    = {Moore, Robert C.},
                title     = {On Log-Likelihood-Ratios and the Significance of Rare
                             Events },
                booktitle = {Proceedings of EMNLP 2004},
                editor = {Dekang Lin and Dekai Wu},
                year      = 2004,
                month     = {July},
                address   = {Barcelona, Spain},
                publisher = {Association for Computational Linguistics},
                pages     = {333--340}
                url = L<>}


Copyright (C) 2000-2006, Ted Pedersen, Satanjeev Banerjee, Amruta Purandare, Bridget Thomson-McInnes and Saiyam Kohli

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to

    The Free Software Foundation, Inc.,
    59 Temple Place - Suite 330,
    Boston, MA  02111-1307, USA.

Note: a copy of the GNU General Public License is available on the web at and is included in this distribution as GPL.txt.