# [R] A dead problem on deriving the derivative equation.

Spencer Graves spencer.graves at pdf.com
Fri Mar 28 04:01:45 CET 2003

```If the limits of integration do not include theta, then you can
interchange the order of integration and differentiation.  To go beyond
this, I think I would need more specifics.

Spencer Graves
p.s.  You've got the negative of the standard KL divergence;  see, e.g.,
"http://www.cis.hut.fi/aapo/papers/NCS99web/node26.html".

Feng Zhang wrote:
> Not for calculation on numbers,
> just to derive the symbolic formulation with
> theta, x..
>
>
> ----- Original Message -----
> From: "Spencer Graves" <spencer.graves at PDF.COM>
> To: "Feng Zhang" <f0z6305 at labs.tamu.edu>
> Cc: <r-help at stat.math.ethz.ch>
> Sent: Thursday, March 27, 2003 6:08 PM
> Subject: Re: [R] A dead problem on deriving the derivative equation.
>
>
>
>>Do you want numbers?  If yes, did you try programming KL(theta) as a
>>function, then computing
>>
>>D.KL <- (KL(theta+delta)-KL(delta))/delta
>>
>>for some suitably small delta?
>>
>>Spencer Graves
>>
>>Feng Zhang wrote:
>>
>>>Hey, R-listers
>>>
>>>I was totally confused by a seemling simple first derivative
>>>function.
>>>Given the Kullback-Leibler divergence function between
>>>a true pdf function P(x,theta) and an approximation pdf
>>>function Q(theta)=q1(theta1)*q2(theta2)*...*qn(thetan),
>>>where theta=[theta1,theta2, ..., thetan]'.
>>>KL(Q||P)
>>>= \integration Q(theta)*log(P(x,theta)/Q(theta)) dtheta
>>>
>>>So how to derive the first derivative of KL with respect
>>>to theta1?
>>>
>>>
>>>Fred
>>>
>>>______________________________________________
>>>R-help at stat.math.ethz.ch mailing list
>>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>>
>>
>
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```