<div>Hi, Lluis, Tina, & Al.,</div>
<div> </div>
<div>Firstly, the math is a little kinky (though Lluis is right--it's roughly OK): it should be 20 * 1M/300K, or 63.3.... </div>
<div> </div>
<div>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.</div>
<div> </div>
<div>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.</div>
<div> </div>
<div>Jim<br><br> </div>
<div><span class="gmail_quote">On 5/15/09, <b class="gmail_sendername">Lluís Padró</b> <<a onclick="return top.js.OpenExtLink(window,event,this)" href="mailto:padro@lsi.upc.edu" target="_blank">padro@lsi.upc.edu</a>> wrote:</span>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">
<div text="#000000" bgcolor="#ffffff">En/na Tina Waldman ha escrit: <span>
<blockquote type="cite">
<div><font face="Arial" size="2">Dear members</font></div>
<div><font face="Arial" size="2">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?</font></div>
<div> </div>
<div><font face="Arial" size="2">Would it be 60 - 20 x 3 ?</font></div>
<div> </div></blockquote></span> As a rough estimate, that may work.<br><br><br> 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<br>
<br> For this and other reasons, relative frequencies seem to be less stable than that when you use larger corpora.<br><br> You can find out more about it in:<br>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.<br>
<br> best,<br><br>
<div>-- <br>
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<td valign="top"><font color="#0000aa"><b>Lluís Padró</b></font><br><font color="#2f2f66">Despatx Ω-S112<br>Campus Nord UPC<br>C/ Jordi Girona 1-3<br>08034 Barcelona, Spain</font></td>
<td valign="top"><font color="#0000aa">Tel: <tt><font size="+1">+34 934 134 015</font></tt><br>Fax: <tt><font size="+1">+34 934 137 833</font></tt></font><br><tt><font size="+1"><a onclick="return top.js.OpenExtLink(window,event,this)" href="mailto:padro@lsi.upc.es" target="_blank">padro@lsi.upc.edu</a><br>
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<font color="#2f2f66">UNIVERSITAT POLITÈCNICA DE CATALUNYA<br>Dept. <a onclick="return top.js.OpenExtLink(window,event,this)" href="http://www.lsi.upc.es/" target="_blank">Llenguatges i Sistemes Informàtics</a><br><a onclick="return top.js.OpenExtLink(window,event,this)" href="http://www.talp.upc.es/" target="_blank">TALP</a> Research Center</font>
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