Text::NSP::Measures::3D::MI::tmi - Perl implementation for True Mutual Information for trigrams.
use Text::NSP::Measures::3D::MI::tmi; $tmi_value = calculateStatistic( n111=>10, n1pp=>40, np1p=>45, npp1=>42, n11p=>20, n1p1=>23, np11=>21, nppp=>100); if( ($errorCode = getErrorCode())) { print STDERR $erroCode." - ".getErrorMessage()."\n"; } else { print getStatisticName."value for bigram is ".$tmi_value."\n"; }
True Mutual Information (tmi) is defined as the weighted average of the pointwise mutual informations for all the observed and expected value pairs.
tmi = [n111/nppp * log(n111/m111) + n112/nppp * log(n112/m112) + n121/nppp * log(n121/m121) + n122/nppp * log(n122/m122) + n211/nppp * log(n211/m211) + n212/nppp * log(n212/m212) + n221/nppp * log(n221/m221) + n222/nppp * log(n222/m222)] PMI = log (n111/m111)
Here n111 represents the observed value for the cell (1,1,1) and m111 represents the expected value for that cell. 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:
n1pp * np1p * npp1 m111= -------------------- nppp
INPUT PARAMS : $count_values .. Reference of an hash containing the count values computed by the count.pl program.
RETURN VALUES : $tmi .. TMI value for this trigram.
INPUT PARAMS : none
RETURN VALUES : $name .. Name of the measure.
Ted Pedersen, University of Minnesota Duluth <tpederse@d.umn.edu>
Satanjeev Banerjee, Carnegie Mellon University <satanjeev@cmu.edu>
Amruta Purandare, University of Pittsburgh <amruta@cs.pitt.edu>
Bridget Thomson-McInnes, University of Minnesota Twin Cities <bthompson@d.umn.edu>
Saiyam Kohli, University of Minnesota Duluth <kohli003@d.umn.edu>
Last updated: $Id: tmi.pm,v 1.10 2006/06/21 11:10:53 saiyam_kohli Exp $
@inproceedings{moore:2004:EMNLP, 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<http://acl.ldc.upenn.edu/acl2004/emnlp/pdf/Moore.pdf>}
http://groups.yahoo.com/group/ngram/
http://www.d.umn.edu/~tpederse/nsp.html
Copyright (C) 2000-2006, Ted Pedersen, Satanjeev Banerjee, Amruta Purandare, Bridget Thomson-McInnes and Saiyam Kohli
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