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

Feng Zhang f0z6305 at labs.tamu.edu
Fri Mar 28 05:18:41 CET 2003

```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?
> >