[R] parallel REML computation

[Liaw, Andy]

Sorry for the off-topic (non-R) post.  Has anyone seen/tried this (from this
week's NA-digest)?

Andy
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From: Joel Malard <JM.Malard at pnl.gov>
Date: Sat, 01 May 2004 15:31:15 -0700
Subject: ACRE, Parallel Covariance Component Estimation Code

A couple of people have asked recently for a copy of the parallel
(restricted/residual) maximum (REML/ML) gradient algorithms from the paper:

    J.M. Malard, "Parallel Restricted Maximum Likelihood Estimation
    for Linear models with a Dense Exogenous Matrix", Parallel
    Computing, 28, pp343-53, 2002. 

The code has been upgraded to PETSc 2.2.0 and TAO 1.6 and is available
by sending an email at acre-developers at eml.pnl.gov. This software solves
covariance component estimation problems for linear models were the
residual vector comes from a normal distribution. The Cholesky
factorization of the covariance matrix is a sparse matrix. The problem
must be framed in the following form, which underlines that REML and ML
estimation can be viewed as a next step in complexity after solving
linear least squares.

    Given a dense matrix A and a response vector b, find the
    Best Linear Unbiased Estimator x and an upper triangular
    matrix L such that Ax=b+e and the matrix LL' (L times
    the transpose of L) is equal to the expected value of xx'.
    Both L and A are assumed full rank. 
 
It is customary in statistical modeling to split the matrix A into fixed
and random effects. The two formulations are equivalent but no script is
provided to do the conversion. 

The purpose of this project was to demonstrate that linear estimation
algorithms such as REML can scale to a few hundred processors on a
distributed memory platform. The dll webpage
http://csm.pnl.gov/statistics/dll contains some additional information. 

If anyone needs an implementation of the REML Hessian matrix using the
forward differentiation mode, it has existed in the past, send an email
to the above address. My current priority is to allow for a singular
matrix L. Comments, bugs reports and suggestions are welcome at the same
email address.

With best regards,

Joel M. Malard, Ph.D.
Pacific Northwest National Laboratory
Battelle Boulevard, PO Box 999
Mail Stop K1-85
Richland, WA 99352



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