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 > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.