Have you tried reparameterizing, using logb (=log(b)) instead of b? Bill Dunlap TIBCO Software wdunlap tibco.com
On Sun, Nov 6, 2016 at 1:17 PM, Rolf Turner <r.tur...@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 > > ______________________________________________ > R-help@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/posti > ng-guide.html > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ R-help@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.
