How to choose Gaussian basis functions hyperparame

问题:

I'm quite new in machine learning environment, and I'm trying to understand properly some basis concept. My problem is the following: I have a set of data observation and the corresponding target values {x,t}. I'm trying to train a function with this data in order to predict the value of unobserved data and I'm trying to achieve this by using the maximum posterior (MAP) technique (and so Bayesian approach) with Gaussian basis function of the form:

\{Phi}Gaussian_{j}(x)=exp((x−μ_{j})^2/2*sigma_{j}^2)

How can I choose

1) The number of basis functions to use (M)

2) The mean for every function (μ_{j})

3) The variance for every function (sigma_{j})

?

回答1:

There are different approaches to this in the literature. The most common approach is to perform an unsupervised clustering of the input data (see the Netlab toolbox). Some other approaches are described in the papers "EMRBF: A Statistical Basis for Using Radial Basis Functions for Process Control" and "Robust Full Bayesian Learning for Radial Basis Networks".