# [R] Dealing with -Inf in a maximisation problem.

William Dunlap wdunlap at tibco.com
Mon Nov 7 20:09:43 CET 2016

```It would be nice if the C functions Rf_logspace_sum, Rf_logspace_add, and
Rf_logspace_sub were available as R functions.  (I wish the '_sub' were
'_subtract' because 'sub' means too many things in R.)

I think Rf_logspace_sum in R could be a little better. E.g., using the C
code

#include <R.h>
#include <Rinternals.h>
#include <Rmath.h>

SEXP Call_logspace_sum(SEXP x)
{
if (TYPEOF(x) != REALSXP)
{
Rf_error("'x' must be a numeric vector");
}
return ScalarReal(Rf_logspace_sum(REAL(x), length(x)));
}

and the R functions

logspace_sum <- function (x) .Call("Call_logspace_sum", as.numeric(x))

and

test <- function (x) {
x <- as.numeric(x)
rbind(Rmpfr = as.numeric(log(sum(exp(Rmpfr::mpfr(x, precBits=5000))))),
Rf_logspace_sum = logspace_sum(x),
subtract_xmax = log(sum(exp(x - max(x)))) + max(x),
naive = log(sum(exp(x))))
}

R-3.3.2 on Linux gives, after options(digits=17)
> test(c(0, -50))
[,1]
Rmpfr           1.9287498479639178e-22
Rf_logspace_sum 1.9287498479639178e-22
subtract_xmax   0.0000000000000000e+00
naive           0.0000000000000000e+00

which is nice, but also the not so nice

> test(c(0, -50, -50))
[,1]
Rmpfr           3.8574996959278356e-22
Rf_logspace_sum 0.0000000000000000e+00
subtract_xmax   0.0000000000000000e+00
naive           0.0000000000000000e+00

With TERR the second test has Rmpfr==Rf_logspace_sum for that example.

Bill Dunlap
TIBCO Software
wdunlap tibco.com

On Mon, Nov 7, 2016 at 3:08 AM, Martin Maechler <maechler at stat.math.ethz.ch>
wrote:

> >>>>> William Dunlap via R-help <r-help at r-project.org>
> >>>>>     on Sun, 6 Nov 2016 20:53:17 -0800 writes:
>
>     > Perhaps the C function Rf_logspace_sum(double *x, int n) would help
> in
>     > computing log(b).  It computes log(sum(exp(x_i))) for i in 1..n,
> avoiding
>     > unnecessary under- and overflow.
>
> Indeed!
>
> I had thought more than twice to also export it to the R level
> notably as we have been using two R level versions in a package
> I maintain ('copula'). They are vectorized there in a way that
> seemed particularly useful to our (Marius Hofert and my) use cases.
>
> More on this -- making these available in R, how exactly? --
> probably should move to the R-devel list.
>
> Thank you Bill for bringing it up!
> Martin
>
>     > Bill Dunlap
>     > TIBCO Software
>     > wdunlap tibco.com
>
>     > On Sun, Nov 6, 2016 at 5:25 PM, Rolf Turner <r.turner at auckland.ac.nz>
> wrote:
>
>     >> On 07/11/16 13:07, William Dunlap wrote:
>     >>
>     >>> Have you tried reparameterizing, using logb (=log(b)) instead of b?
>     >>>
>     >>
>     >> Uh, no.  I don't think that that makes any sense in my context.
>     >>
>     >> The "b" values are probabilities and must satisfy a "sum-to-1"
>     >> constraint.  To accommodate this constraint I re-parametrise via a
>     >> "logistic" style parametrisation --- basically
>     >>
>     >> b_i = exp(z_i)/[sum_j exp(z_j)], j = 1, ... n
>     >>
>     >> with the parameters that the optimiser works with being z_1, ...,
> z_{n-1}
>     >> (and with z_n == 0 for identifiability).  The objective function is
> of the
>     >> form sum_i(a_i * log(b_i)), so I transform back
>     >> from the z_i to the b_i in order calculate the value of the
> objective
>     >> function.  But when the z_i get moderately large-negative, the b_i
> become
>     >> numerically 0 and then log(b_i) becomes -Inf.  And the optimiser
> falls over.
>     >>
>     >> cheers,
>     >>
>     >> Rolf
>     >>
>     >>
>     >>> Bill Dunlap
>     >>> TIBCO Software
>     >>> wdunlap tibco.com <http://tibco.com>
>     >>>
>     >>> On Sun, Nov 6, 2016 at 1:17 PM, Rolf Turner <
> r.turner at auckland.ac.nz
>     >>> <mailto:r.turner at auckland.ac.nz>> wrote:
>     >>>
>     >>>
>     >>> I am trying to deal with a maximisation problem in which it is
>     >>> possible for the objective function to (quite legitimately) return
>     >>> the value -Inf, which causes the numerical optimisers that I have
>     >>> tried to fall over.
>     >>>
>     >>> The -Inf values arise from expressions of the form "a * log(b)",
>     >>> with b = 0.  Under the *starting* values of the parameters, a must
>     >>> equal equal 0 whenever b = 0, so we can legitimately say that a *
>     >>> log(b) = 0 in these circumstances.  However as the maximisation
>     >>> algorithm searches over parameters it is possible for b to take the
>     >>> value 0 for values of
>     >>> a that are strictly positive.  (The values of "a" do not change
> during
>     >>> this search, although they *do* change between "successive
> searches".)
>     >>>
>     >>> Clearly if one is *maximising* the objective then -Inf is not a
> value
>     >>> of
>     >>> particular interest, and we should be able to "move away".  But the
>     >>> optimising function just stops.
>     >>>
>     >>> It is also clear that "moving away" is not a simple task; you can't
>     >>> estimate a gradient or Hessian at a point where the function value
>     >>> is -Inf.
>     >>>
>     >>> Can anyone suggest a way out of this dilemma, perhaps an optimiser
>     >>> that is equipped to cope with -Inf values in some sneaky way?
>     >>>
>     >>> Various ad hoc kludges spring to mind, but they all seem to be
>     >>> fraught with peril.
>     >>>
>     >>> I have tried changing the value returned by the objective function
>     >>> from
>     >>> "v" to exp(v) --- which maps -Inf to 0, which is nice and finite.
>     >>> However this seemed to flatten out the objective surface too much,
>     >>> and the search stalled at the 0 value, which is the antithesis of
>     >>> optimal.
>     >>>
>     >>> The problem arises in a context of applying the EM algorithm where
>     >>> the M-step cannot be carried out explicitly, whence numerical
>     >>> optimisation.
>     >>> I can give more detail if anyone thinks that it could be relevant.
>     >>>
>     >>> I would appreciate advice from younger and wiser heads! :-)
>     >>>
>     >>> cheers,
>     >>>
>     >>> Rolf Turner
>     >>>
>     >>> --
>     >>> Technical Editor ANZJS
>     >>> Department of Statistics
>     >>> University of Auckland
>     >>> Phone: +64-9-373-7599 ext. 88276 <tel:%2B64-9-373-7599%20ext.%2
>     088276>
>     >>>
>     >>> ______________________________________________
>     >>> R-help at r-project.org <mailto:R-help at r-project.org> mailing list --
>     >>> To UNSUBSCRIBE and more, see
>     >>> https://stat.ethz.ch/mailman/listinfo/r-help
>     >>> <https://stat.ethz.ch/mailman/listinfo/r-help>
>     >>> PLEASE do read the posting guide
>     >>> http://www.R-project.org/posting-guide.html
>     >>> <http://www.R-project.org/posting-guide.html>
>     >>> and provide commented, minimal, self-contained, reproducible code.
>     >>>
>     >>>
>     >>>
>     >>
>     >> --
>     >> Technical Editor ANZJS
>     >> Department of Statistics
>     >> University of Auckland
>     >> Phone: +64-9-373-7599 ext. 88276
>     >>
>
>     > [[alternative HTML version deleted]]
>
>     > ______________________________________________
>     > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>     > 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.
>

[[alternative HTML version deleted]]

```

More information about the R-help mailing list