Stas--
Do you know where the ridge is? Can you reparametrize to exploit
prior knowledge of that nature and minimize the use of numerical
techniques? I would also trust your analytical derivatives more as
long as the steps are small; what is the parameter space like?
On Thu, Sep 24, 2009 at 5:17 PM, Stas Kolenikov <[email protected]> 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.
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