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From Ted Dunning <ted.dunn...@gmail.com>
Subject Re: Understanding LogLikelihood Similarity
Date Wed, 30 Apr 2014 22:02:34 GMT
```The contingency table is constructed by looking at how many users have
expressed preference or interest in two items.  If the items are A and B,
the pertinent counts are

k11 - the number of users who interacted with both A and B
k12 - the number of users who interacted with A but not B
k21 - the number of users who interacted with B but not A
k22 - the number of users who interacted with neither A nor B.

These values are values that go into the contingency table and are all that
is needed to compute the LLR value.

See http://tdunning.blogspot.de/2008/03/surprise-and-coincidence.html for a
detailed description.

On Wed, Apr 30, 2014 at 11:31 PM, Mario Levitin <mariolevitin@gmail.com>wrote:

> Hi Ted,
> I have read the paper. I understand the "Likelihood Ratio for Binomial
> Distributions" part.
> However, I cannot make a connection with this part and the contingency
> table.
>
> In order to calculate Likelihood Ratio for two Binomial Distributions you
> need the values: p, p1, p2, k1, k2, n1, n2.
> But the information contained in the contingency table are different from
> these values. So, again, I do not understand how the information contained
> in the contingency table is linked with Likelihood Ratio for Binomial
> Distributions.
>
> In order to find the similarity between two users I tend to think of the
> boolean preferences of user1 as a sample from a binomial distribution and
> the boolean preferences of user2 as another sample from a binomial
> distribution. Then use the LLR to assess how likely these distributions are
> the same. But I don't think this is correct since this calculation does not
> use the contingency table.
>
> I hope my question is clear.
> Thanks.
>
>
>
> On Mon, Apr 28, 2014 at 2:41 AM, Ted Dunning <ted.dunning@gmail.com>
> wrote:
>
> > Excellent.  Look forward to hearing your reactions.
> >
> > On Mon, Apr 28, 2014 at 1:14 AM, Mario Levitin <mariolevitin@gmail.com
> > >wrote:
> >
> > > Not yet, but I will.
> > >
> > > >
> > > > Have you read my original paper on the topic of LLR?  It explains the
> > > > connection with chi^2 measures of association.
> > >
> >
>

```
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