# RBF regression¶

The radial basis function surrogate discipline expresses the model output as a weighted sum of kernel functions centered on the learning input data:

$y = w_1K(\|x-x_1\|;\epsilon) + w_2K(\|x-x_2\|;\epsilon) + ... + w_nK(\|x-x_n\|;\epsilon)$

and the coefficients $$(w_1, w_2, ..., w_n)$$ are estimated by least square regression.

## Dependence¶

The RBF model relies on the Rbf class of the scipy library.

class gemseo.mlearning.regression.rbf.RBFRegression(data, transformer=None, input_names=None, output_names=None, function='multiquadric', der_function=None, epsilon=None, **parameters)[source]

Regression based on radial basis functions.

Constructor.

Parameters
• data (Dataset) – learning dataset

• transformer (dict(str)) – transformation strategy for data groups. If None, do not transform data. Default: None.

• input_names (list(str)) – names of the input variables. Default: None.

• output_names (list(str)) – names of the output variables. Default: None.

• der_function (callable) – derivative of radial basis function, only to be provided if function is callable and not str. The der_function should take three arguments (input_data, norm_input_data, eps). For a RBF of the form function($$r$$), der_function($$x$$, $$|x|$$, $$\epsilon$$) should return $$\epsilon^{-1} x/|x| f'(|x|/\epsilon)$$. Default: None.