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A remarkable feature of this result is that it is valid even for unbounded regression functions and the choice of the temperature parameter depends exclusively on the noise level.
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In the case of the random design nonparametric regression, to correct for the unbounded finite-sample variance of the local polynomial estimator using a 'global' bandwidth, several remedies are available.
In the case of the random design nonparametric regression, to correct for the unbounded finite-sample variance of the local linear estimator (LLE), Seifert and Gasser (J. Amer. Statist. Assoc. 91 (1996) 267 275) apply the idea of ridge regression to the LLE, and propose the local linear ridge regression estimator (LLRRE).
As α goes to 1, the Lapnet becomes lasso logistic regression and the difference becomes unbounded.
However, its properties (unbounded on logarithmic scale) preconditioned its use for further analysis in the regression models.
In the case of the multivariate random design nonparametric regression, an interpolation method is proposed to overcome the problem of unbounded finite sample variance for the local linear estimator (LLE) using a global bandwidth.
Unbounded chatter begets unbounded despair.
The possibilities seem unbounded.
His generosity seemed unbounded.
My admiration for both is unbounded.
Regression is another.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com