[SciPy-User] SciPy-User Digest, Vol 109, Issue 20

The Helmbolds helmrp@yahoo....
Sat Sep 8 12:31:12 CDT 2012


Right you are!! But if the test cases are created using distribution parameters chosen for the test, that will at least supply a check on the result.

Bob and Paula H


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>   1. Re: Optimization Test Cases (josef.pktd@gmail.com)
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>----------------------------------------------------------------------
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>Message: 1
>Date: Sat, 8 Sep 2012 10:22:26 -0400
>From: josef.pktd@gmail.com
>Subject: Re: [SciPy-User] Optimization Test Cases
>To: SciPy Users List <scipy-user@scipy.org>
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>On Sat, Sep 8, 2012 at 8:59 AM, The Helmbolds <helmrp@yahoo.com> wrote:
>> On Mon, Sep 3, 2012 at 6:59 PM, denis <denis-bz-gg@t-online.de> wrote:
>>
>>> Folks,
>>> I'm looking for real or realistic testcases for Nelder-Mead
>>> minimization of noisy functions, 2d to 10d or so, unconstrained
>>> or box constraints, preferably not sum-of-squares and not Rosenbrock et
>>> al.
>>> to wring out a new implementation that has restarts and verbose.
>>> (Would like to discuss ways to restart too
>>> but more ideas than test functions => never converge.)
>>
>> Try some maximum liklihood fitting problems, where parameters are chosen to
>> maximize the likelihood function of some statistical distribution function.
>> All you need for the Weibull case is in the attachment (in Microsoft Word
>> format).
>>
>> Whatever thestatistical distribution you use, I suggest you begin by picking
>> your own values for the parameters (then you'll know what the right answer
>> is). Then generate a sample of values from that distribution/parameter
>> combination. Feed that sample into your optimizatino program, and see if it
>> gives results close to the parameter values you used to generate the sample.
>
>I started my reply in a similar direction:
>
>statsmodels has many cases with minimizing log likelihood.
>
>We don't keep a list of where we ran into problems, but the Negative
>Binomial that Vincent recently coded up has problems with where
>Nelder-Mead wasn't good, and Powell often went way off. (IIRC)
>(fmin_ncg with numerical derivatives works well.)
>
>I have an example with a 3 component mixture distribution (univariate
>with 8 parameters) with lot's of local minima, Nelder Mead is
>sensitive to starting values, but it will take a bit more time to
>clean it my code.
>---------
>
>But I got distracted before checking whether I remember the details correctly.
>
>we have two kinds of problems with Nelder-Mead in maximum likelihood:
>one is the usual getting stuck in local minima
>the other one is that Nelder-Mead stops at something where the
>gradient is not very close to zero, which then might not even be a
>real local minimum.
>
>(on the other hand it's more robust when the starting values are not
>good, and it's slow.)
>
>Josef
>
>
>>
>> Bob and Paula H
>>
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