LinearSmootherGeneralizedCVScorer#
- class skfda.preprocessing.smoothing.validation.LinearSmootherGeneralizedCVScorer(penalization_function=None)[source]#
Generalized cross validation scoring method for linear smoothers.
It calculates the general cross validation score for every sample in a FDataGrid object given a smoothing matrix \(\mathbf{S}(h)\) calculated with a parameter \(h\):
\[GCV(h)=\Xi(\mathbf{S}(h))\frac{1}{M} \sum_{m=1}^{M} \left(x(t_m) - \hat{x}(t_m; h)\right)^2,\]Where \(\hat{x}(t_m; h)\) is the adjusted \(x(t_m)\) and \(\Xi\) is a penalization function. By default the penalization function is:
\[\Xi(\mathbf{S}(h)) = \frac{1}{(1 - \text{tr}(\mathbf{S}(h))/M)^2}.\]but others such as the Akaike’s information criterion can be considered.
- Parameters:
- Returns:
Cross validation score, with negative sign, as it is a penalization.
- Return type:
Methods
Examples using skfda.preprocessing.smoothing.validation.LinearSmootherGeneralizedCVScorer
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Kernel Smoothing