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Re: st: mata optimize with d2debug

From   Partha Deb <[email protected]>
To   [email protected]
Subject   Re: st: mata optimize with d2debug
Date   Fri, 25 Sep 2009 11:19:38 -0400

Stas - although I have no great insight, I wonder if the numerical derivatives are even meaningful along the ridge. In other words, one might expect mreldif to be big because the numerical derivatives are *not* good approximations to the analytical gradients on the ridge.

In coding up -fmm- , I discovered this feature when the parameters in each component were set to be the same - in that case, it's like being on a ridge because the mixing probabilities are not identified. Stata's numerical derivatives are, then, quite different from the analytical ones. But off that "ridge", the analytical and numerical derivatives are very close.

So, my gut instinct is that, you should not worry about the discrepancies quite so much.



Stas Kolenikov wrote:
I am programming a fairly large model and rather poorly identified
model with a couple dozen parameters in Mata. Documentation on
-mf_optimize- says: "When you have done things right, gradient vectors
will differ by approximately 1e–12 or less and Hessians will differ by
1e–7 or less." I never get there; even a restricted version of the
model that is known to converge well produces mreldifs of about 1e-7
and 1e-4, respectively. The mreldifs for the Hessian might start kinda
high between 1 and 10, but they would eventually go down near the
maximum. For the interesting (and poorly identified) models that I
eventually want to fit, I get mreldifs around 1e-3 to 1e-5 in
gradients for most iterations, while my mreldifs for the Hessian
fluctuate between 1e-3 and 1. In the early steps far from the maximum,
the mreldifs for the Hessian can be as large as 100 or so (that's for
20x20 matrix, remember), but they go down as I converge to the
maximum. Since I am walking along a ridge, I would actually tend to
trust my analytical derivatives more than I do the numeric
derivatives. Is that reasonable? Any advice on this? I tried tighter
convergence criteria, but the results did not change much.

Partha Deb
Professor of Economics
Hunter College
ph:  (212) 772-5435
fax: (212) 772-5398

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