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From Luc Maisonobe <Luc.Maison...@free.fr>
Subject Re: [math] Estimator capabilities
Date Fri, 30 Nov 2007 19:36:44 GMT
luc.maisonobe@free.fr a écrit :
> Selon Al Lelopath <jdaues@gmail.com>:
> 
>> I see that apache commons has Estimators (aka Solvers, yes?):
>> EstimatedParameter
>> GaussNewtonEstimator
>> LevenbergMarquardtEstimator
>> SimpleEstimationProblem
>> WeightedMeasurement
> 
> Not all these classes represent solvers. Only the ones that implement Estimator
> (i.e. GaussNewtonEstimator and LevenbergMarquardtEstimator) are estimators. The
> other classes are used for estimation but are not the solvers themselves.
> EStimatedParameters represent the parameters of the models, and the job of the
> solver is to update these parameters in order to minimize a cost function. When
> the solvers has finished its work, retrieving the results is a matter of reading
> the updated value hold by the instances of this class. SimpleEstimationProblem
> is mostly a container for the parameters and the measurements. The basic usage
> is for the user to create a problem-specific class extending this one, the
> created class implementing the logic of the model (relation between parameters
> and model, relation between model and theoretical measurements, container for
> the observed measurements). The cost function is automatically computed from the
> residuals between theoretical and observed measurements). The
> WeightedMeasurements class represent a measurement, it should also be
> specialized by creating a class extending this one for each type of
> measurements.
>> Our mathematician has specified features we will need:
>> 1. Assume non-negative parameters,
> 
> This feature is a simple bound constraint. The estimators do not
> handle any constraints yet (neither simple bounds, nor linear, nor non-linear).
> This will most probably be added one day as it is rather important.
> 
> Simple bounds constraints can be simulated artificially though, by adding a
> layer between the solved parameters and the real parameters of the model. For
> example, if your model needs three parameters p1, p2 and p3 with p1 that should
> be positive, you can really solve using q1, p2, p3 with an additional transform
> p1 = q1^2 implemented by your model. Similar transforms can be built for double
> bounds constraints.
> 
>> 2. forward and central derivatives,
> 
> The derivatives are not computed by the classes provided by commons-math, they
> should be provided by the user when extending the SimpleEstimationProblem class
> (or implementing directly the EstimationProblem interface if prefered). This
> means you can use any method you prefer for computeing them : forward, central
> or backward finite differences or analycally computed derivatives.
> 
>> 3. tangent estimates
> 
> I'm not sure I understand what you mean here. The solvers are based on gradient
> computation at the current point which is updated according to the selected
> solver algorithm.
> 
>> 4. quadratic estimates,
> 
> I'm also not sure to understand what you mean here. The problem are defined in
> terms of observed measurements which are defined at problem start and
> theoretical measurements which are automatically recomputed during the search as
> the current point moves. The algorithms compute a quadratic cost function as the
> sum of the weighted residuals between theoretical measurements and observed

I meant sum of weighted SQUARED residuals, of course.

> measurements. This cost function is minimized (i.e. parameters are adjusted in
> such a way theoretically recomputed measurements match the observations). The
> quadratic structure of the cost function is fixed, but the measurements involved
> and the weights can be specified by the user.
> 
>> 5. Newton and conjugate search direction
> 
> The GaussNewtonEstimator is based on ... the Gauss-Newton algorithm which
> iterates over a Newton search.
> 
> The LevenbergMarquardtEstimator is a much more elaborate algorithm which
> interpolates between a Gauss-Newton and a gradient method. It is more robust
> than Gauss-Newton and highly recommended.
> 
> Commons-math currently does not yet provide a simple conjugate-gradient method.
> 
> 
>> Does apache commons have these capabilities?
> 
> To conclude, commons-math provide some of these capabilities, but not all of
> them.
> 
> Luc
> 
> 
> 
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