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Re: RBF Toolbox?


From: Jaroslav Hajek
Subject: Re: RBF Toolbox?
Date: Fri, 23 Apr 2010 07:05:53 +0200

2010/4/23 Mike B. <address@hidden>:
> Hi Jordi,
>
> Thanks for the prompt reply.
> I am interested in interpolation from scattered data, dimension (number of 
> components per vector) can be as high as 200. Ideally, the toolbox would 
> allow to select from several types (multiquadric, linear, Gaussian, inverse 
> multiquadric etc.) and would calibrate any hyper-parameters (such as the free 
> coefficient in MQ and IMQ), say, by cross-validation. The DACE toolbox 
> calibrates the Kriging hyper-parameters by maximum likelihood.
>
> Cheers,
> Mike.
>
>

You may want to try the OctGPR package for Gaussian Process
Regression, which essentially is just another name for Kriging.
It supports several covariance models (gaussian, exponential, imq,
matern-3 and matern-5), and can callibrate hyper-parameters by ML. The
hyperparameters consist of a scale factor for each dimension and a
single noise level. Having a separate scale factor for each dimension
typically provides the best results, but may be too costly if there
are many dimensions (I never used it with more than 10).
There is currently no built-in way to employ fewer hyperparams in the
training, except that you can use the function in no-training mode (it
just calculates the log likelihood) and then employ it in any custom
training procedure you like. But the built-in one is faster (takes
care of reusing data in memory and calculates the ML derivatives very
efficiently).

A stupid&simple demo is here (some info may be outdated), and is also
part of the script:
http://artax.karlin.mff.cuni.cz/~hajej2am/octgpr.php

besides the full GPR, which is usable up to several thousands of
scattered points (requires full matrix factorizations), there is also
a projected approach, where the data is projected onto fewer centers
to reduce the rank of covariance matrix and hence reduces the cost
from O(N^3) to O(NM^2), where M is the number of centers. I should
warn you, however, that this part hasn't yet received much testing.

hth


-- 
RNDr. Jaroslav Hajek, PhD
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic
url: www.highegg.matfyz.cz



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