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" <[EMAIL PROTECTED]>
To: "Feng Zhang" <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
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?
Thanks for your helpful advices.
Fred
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