Subject: LBFGS for use in large maximum likelihood problem
From: dlakelan
Date: Fri, 22 Aug 2008 13:04:20 -0700
I've got another set of questions about LBFGS, maximum likelihood, and
numerical issues.
I'm using the inverse of the hessian of the log-likelihood function
evaluated at the maximum likelihood estimates (from LBFGS) to
approximate the uncertainties in the estimated coefficients.
Calculating the hessian directly from the log-likelihood expression
takes thousands of seconds... If i calculate the hessian of one symbolic
term of the sum, apply the "optimize" function, and then numerically
evaluate the sum of the optimized expression it takes a few seconds (8
or so). However optimize says
"`optimize' has met up with a special form - answer may be wrong."
I checked the result against a non-optimized version (which takes 500
seconds or so) and I get the same numerical values.
When should I worry about relying on the "optimize" results?
Also, can I use optimize on the figure of merit expression for LBFGS to
get faster results? Is there a way to hand LBFGS an expression for the
gradient (also optimized)? The manual doesn't mention anything, but I
thought there was some work done on this?
Thanks much,
Dan