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From Mario Levitin <mariolevi...@gmail.com>
Subject Re: Understanding LogLikelihood Similarity
Date Thu, 01 May 2014 17:05:22 GMT
After some thought now I'm in a better situation, but I think it will take
some more effort to fully digest it.
Thanks for your answers Ted.



On Thu, May 1, 2014 at 2:21 AM, Ted Dunning <ted.dunning@gmail.com> wrote:

> OK.
>
> Whether a user has interacted with A is a sample from a binomial
> distribution with an unknown parameter p_A.  Likewise with B and p_B.  The
> two binomial distributions may or may not be independent.
>
> The LLR is measuring the degree evidence against independence.
>
>
>
>
> On Thu, May 1, 2014 at 12:50 AM, Mario Levitin <mariolevitin@gmail.com
> >wrote:
>
> > Ted, I understand how the contingency table is constructed, and how to
> > compute the LLR value. What I cannot understand is how to link this with
> > binomial distributions.
> >
> >
> > On Thu, May 1, 2014 at 1:02 AM, Ted Dunning <ted.dunning@gmail.com>
> wrote:
> >
> > > 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.htmlfor
> > > 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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