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Re: RBF Toolbox?
From: |
Mike B. |
Subject: |
Re: RBF Toolbox? |
Date: |
Sun, 25 Apr 2010 18:42:59 -0700 (PDT) |
--- On Fri, 23/4/10, Jordi Gutiérrez Hermoso <address@hidden> wrote:
> This sounds fairly simple to implement, except I don't know
> what
> cross-validation is. I thought picking the right parameters
> for the
> RBFs was still a dark art. Also, what's a linear RBF? Do
> you mean the
> polynomial/conical RBFs? Got a reference for me?
Selecting the RBF hyper-parameter is definitely not black-magic and is covered
extensively under statistical model-selection (a few references floating
around, no particular order):
* Rippa, An Algorithm for Selecting a Good Value for the Parameter c in Radial
Basis Function Interpolation
* Golberg et al., Improved Multiquadric Approximation for Partial Differential
Equations
* Tenne and Armfield, A Memetic Algorithm Assisted by an Adaptive Topology
Artificial Neural Network and Variable Local Models for Expensive Optimization
Problems
* Milroy et al., An Adaptive Radial Basis Function Approach to Modeling
Scattered Data
The main methods (which I know of) are maximum likelihood, cross-validation
(essentially an empirical ML) and bootstrap (computationally intensive). There
is no `optimal' method and they all should provide `good' and similar estimates
so small differences may not be crucial. A major consideration is how
computationally-efficient is the method. You might want to allow the user to
select their method of choice.
For reviews on RBFs:
* Powell, Radial Basis Function Methods for Interpolation of Functions of Many
Variables
* Buhmann, Radial Basis Functions Theory and Implementations
Cheers.