Hi, Deepayan:
On 2021-03-13 01:27, Deepayan Sarkar wrote:
On Sat, Mar 13, 2021 at 10:08 AM Spencer Graves
<spencer.gra...@effectivedefense.org> wrote:
TWO COMMENTS:
1. DID YOU ASSIGN THE OUTPUT OF "optim" to an object, like "est <-
optim(...)"? If yes and if "optim" terminated normally, the 60,000+
paramters should be there as est$par. See the documentation on "optim".
2. WHAT PROBLEM ARE YOU TRYING TO SOLVE?
I hope you will forgive me for being blunt (or perhaps bigoted), but
I'm skeptical about anyone wanting to use optim to estimate 60,000+
parameters. With a situation like that, I think you would be wise to
recast the problem as one in which those 60,000+ parameters are sampled
from some hyperdistribution characterized by a small number of
hyperparameters. Then write a model where your observations are sampled
from distribution(s) controlled by these random parameters. Then
multiply the likelihood of the observations by the likelihood of the
hyperdistribution and integrate out the 60,000+ parameters, leaving only
a small number hyperparameters.
Just a comment on this comment: I think it's perfectly reasonable to
optimize 60k+ parameters with conjugate gradient. CG was originally
developed to solve linear equations of the form Ax=b. If x was not
large in size, one would just use solve(A, b) instead of an iterative
method.
Use of CG is quite common in image processing. A relatively small
300x300 image will give you 90k parameters.
-Deepayan
Thanks for this.
If both A and b are 300x300, then x will also be 300x300.
What do you do in this case if A is not square or even ill
conditioned?
Do you care if you get only one of many possible or approximate
solutions, and the algorithm spends most of its time making adjustments
in a singular subspace that would have best been avoided?
Spencer
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