Text::NSP::Measures::4D::MI::ll - Perl module that implements Loglikelihood measure of association for 4-grams.
$ll_value = calculateStatistic( n1111=>8, n1ppp=>306, np1pp=>83, npp1p=>83, nppp1=>57, n11pp=>8, n1p1p=>8, n1pp1=>8, np11p=>83, np1p1=>56, npp11=>56, n111p=>8, n11p1=>8, n1p11=>8, np111=>56, npppp=>15180); if( ($errorCode = getErrorCode())) { print STDERR $erroCode." - ".getErrorMessage()."\n"; } else { print getStatisticName."value for 4-gram is ".$ll_value."\n"; }
The log-likelihood ratio measures the devitation between the observed data and what would be expected if <word1>, <word2>, <word3> and <word4> were independent.The higher the score, the less evidence there is in favor of concluding thatthe words are independent.
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:
n1ppp * np1pp * npp1p * nppp1 m111= ------------------------------- npppp ^ 3
Then the deviation between observed and expected values for each internal cell is computed to arrive at the log-likelihood value.
Log-Likelihood = 2 * [n1111 * log ( n1111 / m1111 ) + n1112 * log ( n1112 / m1112 ) + n1121 * log ( n1121 / m1121 ) + n1122 * log ( n1122 / m1122 ) + n1211 * log ( n1211 / m1211 ) + n1212 * log ( n1212 / m1212 ) + n1221 * log ( n1221 / m1221 ) + n1222 * log ( n1222 / m1222 ) + n2111 * log ( n2111 / m2111 ) + n2112 * log ( n2112 / m2112 ) + n2121 * log ( n2121 / m2121 ) + n2122 * log ( n2122 / m2122 ) + n2211 * log ( n2211 / m2211 ) + n2212 * log ( n2212 / m2212 ) + n2221 * log ( n2221 / m2221 ) + n2222 * log ( n2222 / m2222 )];
INPUT PARAMS : $count_values .. Reference of an hash containing the count values computed by the count.pl program.
RETURN VALUES : $loglikelihood .. Loglikelihood value for this 4-gram.
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 <bthomson@cs.umn.edu>
Saiyam Kohli, University of Minnesota Duluth <kohli003@d.umn.edu>
Last updated: $Id: ll.pm,v 1.1 2008/11/22 18:53:13 btmcinnes Exp $
@article{Dunning93, author = {Dunning, T.}, title = {Accurate Methods for the Statistics of Surprise and Coincidence}, journal = {Computational Linguistics}, volume = {19}, number = {1}, year = {1993}, pages = {61-74} url = L<http://www.comp.lancs.ac.uk/ucrel/papers/tedstats.pdf>} @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>}
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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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