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

Spencer Graves spencer.graves at pdf.com
Fri Mar 28 03:08:56 CET 2003

```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?
>
> Thanks for your helpful advices.
>
> Fred
>
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> R-help at stat.math.ethz.ch mailing list
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```

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