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st: Re: st: Searching for Kullback–Leiber divergence


From   Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: st: Searching for Kullback–Leiber divergence
Date   Sun, 9 May 2010 23:02:41 +0530

Michael,

That, I think, is a slightly harder problem. See here and the references within:
http://www.tsc.uc3m.es/~fernando/bare_conf3.pdf

Most of these references ([21], [12], [5], [22], [13], [18]) are
recent and fairly involved. If you have an algorithm in mind that
would be very helpful in answering your question/supplying you with
code. Eqn (4) in the link above is fairly easily programmable.

However, it would be much easier if I could see what you have in mind
in situ, so a reference to an application would be great.

T

2010/5/9 Michael C. Morrison <Morrimic@niacc.edu>
>
> Tirthankar Chakravarty advised that I look into -multigof- for the Kullback–Leiber divergence. Thanks for the response but -multigof- is not what I'm looking for.
>
> Kullback–Leiber divergence is sometimes referred to as 'relative entropy' or 'cross entropy'. The Kullback–Leiber divergence that I need summarizes the effect of location and shape changes on the overall relative distribution involving two continuous distributions. The Kullback–Leiber divergence has a simple interpretation in terms of the relative distribution, and it is decomposable into the location, shape and other components.
>
> I have - reldist-. It  does a great job in plotting relative & cumulative pdfs, location/shape shift changes, polarization coefficients, but it doesn't provide a measure of the overall distributional difference between two distributions. That's where the The Kullback–Leiber divergence comes to the rescue. The advantage of the Kullback–Leiber divergence is that it is decomposable.
>
> Hope this clarifies what I'm searching for.
>
> Mike
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--
To every ω-consistent recursive class κ of formulae there correspond
recursive class signs r, such that neither v Gen r nor Neg(v Gen r)
belongs to Flg(κ) (where v is the free variable of r).

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