[R-sig-ME] Speed estimation for lmer?

[Adam D. I. Kramer]

On Thu, 11 Sep 2008, Douglas Bates wrote:

>> ...I assume that this means that for iteration 0, those are the estimated
>> parameters, and there are 36 of them. It appears to be completing an
>> iteration every 15-20 seconds. The full interaction should estimate 8
>> variances and sum(1:7) = 28 covariances = 36 parameters total, so that
>> checks out. 36 parameters is 3.6 times as many as fm2 required, so
>> 312.860*3.6 = 1126, or about 18 minutes to fit...far less than it's
>> taken.
>
>> 36^2 / 10^2 = 13 times longer, or about 68 minutes to fit fm3...we'll see
>> when we get there.
>
> There are two ways in which this will take longer.  Each iteration will
> take longer and it will probably take many more iterations.  A 36
> parameter optimization problem is a big problem.  Optimization usually
> doesn't scale linearly.  Worst case it is exponential in the length of the
> parameter vector.  Most optimization algorithms can do better than that
> but the complexity is still on the order of p^3 or more.

(269 iterations over 106 minutes and counting). A jump from p^10=312 seconds
to p^36 suggests that the model will probably never end up fit; p^3 suggests
243 minutes total (132 minutes from now).

>>> However, I would check both with and without accelerated BLAS if you
>>> have a multi-core processor.  Sometimes a multithreaded accelerated BLAS
>>> can make lmer run slower, not faster. This is because the calls to the
>>> BLAS are predominantly for small matrices and the communications
>>> overhead for multithreaded versions more than offsets the performance
>>> gain from using multiple cores.
>
>> Interesting...I hadn't thought of that. The processor is 4-core, and R
>> was linked against the multithreaded BLAS. This may be covered in a faq
>> somewhere, but is there an easy way to swap out the BLAS that R is
>> accessing? Perhaps renaming my libraries is sufficient?
>
> There is some discussion in the "Administration" manual about this. Rather
> than trying to hot swap the libraries I would probably reconfigure and
> recompile.  Configure using --with-blas=no and --with-lapack=no.

This section in the R-admin manual confused me.

Just to be clear, if I do this, then the BLAS library set in BLAS_LIBS *at
runtime* will be used, or at compile time? Or are you suggesting I build
another version of R which uses non-threaded ATLAS? Or a version of R that
uses its own BLAS?

--Adam