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From Andreas Niekler <>
Subject Re: [math] Usage of DifferentiableMultivariateRealFunction
Date Mon, 14 May 2012 14:36:05 GMT
Thank you all very much.

I have updated my DifferentiableMultivariateRealFunction and this is 
what it looks like now (appended). I use this and stick it into a 
MultiStartDifferentiableMultivariateRealOptimizer. Unfortunately this 
procedure end with the creation of some negative parameters (impossible 
by method) which i cannot oversee right now (wrong gradients, wrong 
procedure?). Here is the procedure i'm using. Hope this clarifies my 
task and maybe to get some more hints to optimize my usage of commons Math:

parameter[2] = 1.0;
parameter[1] = 1.0;
parameter[0] = 1.0;
					NonLinearConjugateGradientOptimizer underlying = new 
JDKRandomGenerator g = new JDKRandomGenerator();
RandomVectorGenerator generator =
new UncorrelatedRandomVectorGenerator(3, new GaussianRandomGenerator(g));
				 MultiStartDifferentiableMultivariateRealOptimizer optimizer = new 
MultiStartDifferentiableMultivariateRealOptimizer(underlying, 10, 
								    GaussianProcessRegressionMarginalLikelihood gprml = new 
GaussianProcessRegressionMarginalLikelihood(input, X);
RealPointValuePair pair = null;
try {
pair = optimizer.optimize(gprml, GoalType.MAXIMIZE, parameter);
} catch (OptimizationException e) {
// TODO Auto-generated catch block
} catch (FunctionEvaluationException e) {
// TODO Auto-generated catch block

Am 14.05.2012 15:42, schrieb Luc Maisonobe:
> Le 14/05/2012 14:11, Andreas Niekler a écrit :
>> Hello,
> Hi Andreas,
>> after reading a lot through the tutorial this is the code that i came up
>> with regarding the implementation of a gaussian process regression
>> optimisation (File appended):
>> initCovarianceAndGradients(): initialisation of matrices and
>> calculations which are needed by both marginal likelihood calculation
>> and gradient calculation:
>> Within this function i calculate some things globally which are strongly
>> reused by the value() and gradient() functions. What i do not really
>> understand is the passing of the double[] argument to the value()
>> function and the value() function of the gradient() method. Are those
>> methods called by the optimizer with the updated parameters? If this is
>> the case i have to recalculate the global calculations with each call to
>> the value() and gradient() methods.
> Yes, the double[] argument is updated at each call and correspond to the
> current estimate as the algorithm iterates towards the solution.
> You cannot even rely on the calls being always scheduled in the same
> way. As an example, the Gauss-Newton optimizer performs the two calls
> with function first and gradient afterwards at each iteration, but the
> Levenberg-Marquardt optimizer has two embedded loops and computes
> Jacobians on the external loop and the function value on the internal
> loop. So you should probably not compute everything beforehand in the
> hope it will be used later on.
> Luc
>> Thanks for clarification
>> Am 14.05.2012 12:53, schrieb Gilles Sadowski:
>>> Hello.
>>>>> thanks for the reply. But i wonder what is the input for value and
>>>>> gradient.
>>>>> in DifferentiableMultivariateRealFunction this needs to be a double
>>>>> array
>>>>> but what needs to be provided there? The parameters for the function
>>>>> optimize?
>>>>> Thank you very much again
>>>>> Andreas
>>>> Do please have a look to the examples, as your question (and my
>>>> answer) is too vague if not supported by proper code. I guess the
>>>> answer to your question is 'yes', the double[] array is indeed the set
>>>> of parameters, but again, do check the examples, I would not like to
>>>> be misguiding you. Besides the user guide which should provide you
>>>> with the answer, have a look to this implementation [1], line 153. In
>>>> this implementation, x[i] and y[i] are the data points, yhat[i] are
>>>> the model predictions, and a[] are the parameters. You should be able
>>>> to find your way with this example.
>>> I've also just added another bit of code show-casing the usage of the
>>> "non-linear least-squares" optimizers (svn revision 1338144).
>>> Best regards,
>>> Gilles
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Dipl.-Ing. (FH) Andreas Niekler
Mitarbeiter und Promovend
Bereich Multimedia-Produktionssysteme und -technologien

Hochschule für Technik, Wirtschaft und Kultur Leipzig
Fachbereich Medien

Gustav-Freytag-Straße 40
04277 Leipzig

Telefon: +49 0341 30 76 2378


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