## Asymptotics of Gaussian Regularized Least-Squares

##### Author(s)

Lippert, Ross; Rifkin, Ryan
DownloadMIT-CSAIL-TR-2005-067.ps (7116.Kb)

##### Additional downloads

##### Metadata

Show full item record##### Abstract

We consider regularized least-squares (RLS) with a Gaussian kernel. Weprove that if we let the Gaussian bandwidth $\sigma \rightarrow\infty$ while letting the regularization parameter $\lambda\rightarrow 0$, the RLS solution tends to a polynomial whose order iscontrolled by the relative rates of decay of $\frac{1}{\sigma^2}$ and$\lambda$: if $\lambda = \sigma^{-(2k+1)}$, then, as $\sigma \rightarrow\infty$, the RLS solution tends to the $k$th order polynomial withminimal empirical error. We illustrate the result with an example.

##### Date issued

2005-10-20##### Other identifiers

MIT-CSAIL-TR-2005-067

AIM-2005-030

CBCL-257

##### Series/Report no.

Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory

##### Keywords

AI, machine learning, regularization