I suggest you try to translate your constraints into an
unconstrained constrained problem using logarithms, then do "nonlinear
mixed effects modeling" as described in chapters 6-8 of Pinheiro and
Bates (2000). To do this, I would first start with the simpler linear
estimation problem to get starting values for the nonlinear estimation.
You should be able to do this using the "nlme" function in the "nlme"
package. If you have trouble with this, you might consider the "nlmer"
function in the "lme4" package. The latter is newer and better in many
ways but not as well documented.
Hope this helps.
Spencer Graves
avraham.ad...@guycarp.com wrote:
Thank you both very much for your replies. What makes this a little less
straightforward, at least to me, is that there needs to be constraints on
the solved parameters. They most certainly need to be positive and there
may be an upper limit as well. The true best linear fit would have negative
entries for some of the parameters.
Originally, I was using the L-BFGS-B method of optim which both allows for
box constraints and has the limited memory advantage useful when dealing
with large matrices. Having the analytic gradient, I thought of using BFGS
and having a statement in the function returning "Inf" for any parameters
outside the allowable constraints.
I do /not/ know how to apply parameter constraints when using linear
models. I looked around at the various manuals and help features, and
outside of package "glmc" I did not find anything I could use. Perhaps I
overlooked something. If there is something I missed, please let me know.
If there truly is no standard optimization routine that works on sparse
matrices, my next step may be to use the normal equations to shrink the
size of the matrix, recast it as a dense matrix (it would only be 1173x1173
then) and then hand it off to optim.
Any further suggestions or corrections would be very much appreciated.
Thank you,
--Avraham Adler
Douglas Bates
<ba...@stat.wisc.
edu> To
Sent by: avraham.ad...@guycarp.com
dmba...@gmail.com cc
r-help@r-project.org
Subject
05/15/2009 11:57 Re: [R] Optimization algorithm to
AM be applied to S4 classes -
specifically sparse matrices
On Wed, May 13, 2009 at 5:21 PM, <avraham.ad...@guycarp.com> wrote:
Hello.
I am trying to optimize a set of parameters using /optim/ in which the
actual function to be minimized contains matrix multiplication and is of
the form:
SUM ((A%*%X - B)^2)
where A is a matrix and X and B are vectors, with X as parameter vector.
As Spencer Graves pointed out, what you are describing here is a
linear least squares problem, which has a direct (i.e. non-iterative)
solution. A comparison of the speed of various ways of solving such a
system is given in one of the vignettes in the Matrix package.
This has worked well so far. Recently, I was given a data set A of size
360440 x 1173, which could not be handled as a normal matrix. I brought
it
into 'R' as a sparse matrix (dgCMatrix - using sparseMatrix from the
Matrix
package), and the formulæ and gradient work, but /optim/ returns an error
of the form "no method for coercing this S4 class to a vector".
If you just want the least squares solution X then
X <- solve(crossprod(A), crossprod(A, B))
will likely be the fastest method where A is the sparse matrix.
I do feel obligated to point out that the least squares solution for
such large systems is rarely a sensible solution to the underlying
problem. If you have over 1000 columns in A and it is very sparse
then likely at least parts of A are based on indicator columns for a
categorical variable. In such situations a model with random effects
for the category is often preferable to the fixed-effects model you
are fitting.
After briefly looking into methods and classes, I realize I am in way
over
my head. Is there any way I could use /optim/ or another optimization
algorithm, on sparse matrices?
Thank you very much,
--Avraham Adler
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