[Corpora-List] extrapolating to 1 million

[James L. Fidelholtz]

Hi, Lluis, Tina, & Al.,

Firstly, the math is a little kinky (though Lluis is right--it's roughly
OK): it should be 20 * 1M/300K, or 63.3....

The point Lluis makes about the corpus containing more rarer words as we
augment the size of the corpus is, of course, correct. Nevertheless (here I
haven't done much work, but I just appeal to common sense and the 'law of
large numbers' (not sure this is relevant, but 300K is a *pretty* large
number)), we should expect, even with more obscure words to muddy up the
picture, that the percentage of *common* words in the 300K corpus should be
roughly the same in a corpus of 1M words, especially (but not quite only,
for the more common words) if the corpora are selected from similar
universes. Naturally, different selection criteria might affect even very
common words, and it has been shown many times that the 'rarer' the words
are, the more variable the exact percentage can be, but I wouldn't expect a
priori that ever bigger corpora should lower the percentages of common (or
even necessarily of rare) words. Indeed, for the hapax legomena, say, that
enter in the new 'complement' to the corpus, their percentage even
*increases* from 0 to 0.0001, correspondingly more for the other new words.

Of course there can always be variations in the percentages. But, equally
always, we *expect* that our sampling of the universe will give us for a
word W something reasonably close to its real percentage frequency. And that
when we repeat the process (or augment it), we will again get reasonably
close to its 'real' frequency, so that we expect both frequencies to be
close to each other. The real world often lets us down (and don't bet the
family farm on any of this), but I guess statisticians tend to be optimists
in this regard. And mathematicians even more (after all, we have an edge,
and so tend to gain 5 family farms for each one we lose). In this sense,
think: Bell curve, which, with the appropriate tweaks, is the exact
representation of what our expectations should be in a particular case.

Jim


On 5/15/09, Lluís Padró <padro at lsi.upc.edu> wrote:
>
> En/na Tina Waldman ha escrit:
>
> Dear members
> Could you tell me what the frequency would be in a corpus of 1 million if I
> extrapolated from the frequency of  20 in a corpus of 300K?
>
> Would it be 60 - 20 x 3 ?
>
>
>    As a rough estimate, that may work.
>
>
>    Nevertheless, due to Zipf's laws, when you go from 300K to 1M, you're
> getting lots of previously unseen words with very low frequencies, but they
> modify the proability distribution
>
>    For this and other reasons, relative frequencies seem to be less stable
> than that when you use larger corpora.
>
>    You can find out more about it in:
> Baroni M., Evert S., "Words and echoes: assessing and mitigating the
> non-randomness problem in word frequency distribution modeling".
> In:Proceedings of ACL 2007, East Stroudsburg PA: ACL, 2007. p. 904-911, Atti
> del convegno: "Association for Computational Linguistics (ACL)", Prague,
> 23rd-30th June 2007.
>
>    best,
>
> --
>   ------------------------------
>  *Lluís Padró*
> Despatx Ω-S112
> Campus Nord UPC
> C/ Jordi Girona 1-3
> 08034 Barcelona, Spain Tel: +34 934 134 015
> Fax: +34 934 137 833
> padro at lsi.upc.edu <padro at lsi.upc.es>
> www.lsi.upc.edu/~padro <http://www.lsi.upc.es/~padro>
> ------------------------------
> UNIVERSITAT POLITÈCNICA DE CATALUNYA
> Dept. Llenguatges i Sistemes Informàtics <http://www.lsi.upc.es/>
> TALP <http://www.talp.upc.es/> Research Center
> ------------------------------
>
> _______________________________________________
> Corpora mailing list
> Corpora at uib.no
> http://mailman.uib.no/listinfo/corpora
>
>


-- 
James L. Fidelholtz
Posgrado en Ciencias del Lenguaje
Instituto de Ciencias Sociales y Humanidades
Benemérita Universidad Autónoma de Puebla, MÉXICO
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://listserv.linguistlist.org/pipermail/corpora/attachments/20090515/82075e6e/attachment.htm>
-------------- next part --------------
_______________________________________________
Corpora mailing list
Corpora at uib.no
http://mailman.uib.no/listinfo/corpora