My understanding: Yes, the log-likelihood ratio (-2 log lambda) follows a chi-squared distribution with 1 degree of freedom in the 2x2 table case. A ~A B ~B
We're testing to see if p(A | B) = p(A | ~B). That's the null hypothesis. I compute the LLR. The larger that is, the more unlikely the null hypothesis is to be true. I can then look at a table with df=1. And I'd get p, the probability of seeing that result or something worse (the upper tail). So, the probability of them being similar is 1 - p (which is exactly the CDF for that value of X). Now, my question is: in the contingency table case, why would I normalize? It's a ratio already, isn't it? On Thu, Jun 20, 2013 at 11:03 AM, Sean Owen <sro...@gmail.com> wrote: > someone can check my facts here, but the log-likelihood ratio follows > a chi-square distribution. You can figure an actual probability from > that in the usual way, from its CDF. You would need to tweak the code > you see in the project to compute an actual LLR by normalizing the > input. > > You could use 1-p then as a similarity metric. > > This also isn't how the test statistic is turned into a similarity > metric in the project now. But 1-p sounds nicer. Maybe the historical > reason was speed, or, ignorance. > > On Thu, Jun 20, 2013 at 8:53 AM, Dan Filimon > <dangeorge.fili...@gmail.com> wrote: > > When computing item-item similarity using the log-likelihood similarity > > [1], can I simply apply a sigmoid do the resulting values to get the > > probability that two items are similar? > > > > Is there any other processing I need to do? > > > > Thanks! > > > > [1] http://tdunning.blogspot.ro/2008/03/surprise-and-coincidence.html >