       Optimization doing more function evaluations than claimed?

• To: mathgroup at smc.vnet.net
• Subject: [mg57197] Optimization doing more function evaluations than claimed?
• From: Gareth Russell <gjr2008 at columbia.edu>
• Date: Fri, 20 May 2005 04:43:46 -0400 (EDT)
• Organization: Columbia University
• Sender: owner-wri-mathgroup at wolfram.com

```Hi All,

I have been using FindMaximize without symbolic derivatives to maximize
a likelihood function that operates on a large dataset. Because the
process is slow, I want to track progress as it happens, so I include a
Print[{parameter1, parameter2, ..., likelihood}] step in the function
being evaluated. In doing so, I have noticed that the function appears
to be evaluated twice for each trial of the parameter values. When I
look at diagnostics after the fit is complete, such as the output of
the EvaluationMonitor option, it shows each trial only once. For
example, if Mathematica claims 20 steps after the fact, the number of
printed outputs is always 40, in identical pairs. The 40 outputs appear
evenly spaced in time, and the total timing of the fitting process,
compared to the timing of one evaluation of the function, confirms that
indeed, it was evaluated 40 times.

Does anyone know why (i.e., under what conditions) FindMinimum might do
this? You won't be able to evaluate my function, as it calls the
datasets, but here it is anyway, with some info:

lDistExp[distMaps_, e_, b1_?NumericQ] := Module[{distQ,
pMaps, logList, logLike},
distQ = mapExponential2[distMaps, b1];
pMaps = Map[toProbs[#] &, distQ];
logList = Log[MapThread[#1[[#2]] &, {pMaps, e}]];
loglike=Apply[Plus, logList];
Print[{b1,logLike}];
logLike
]

distMaps is a (large) matrix of reals, e is a vector of integers, and
b1 is a real.

The functions mapExponential2[] and toProbs[] are compiled functions
(for speed).

The function is maximized with respect to b1.

As a side note that may be relevant, if I load the
Optimization`UnconstrainedProblems` package and use the FindMinimumPlot
function, the target function is be evaluated THREE times per step,
even though the output again says just 20 steps.

Because the fitting procedure is necessarily slow because of dataset
size, I don't want to be doing more function evaluations than are
necessary!

Thanks,

Gareth Russell
Columbia University

```

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