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Asymptotics of Gaussian Regularized Least-Squares

Author(s)
Lippert, Ross; Rifkin, Ryan
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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
URI
http://hdl.handle.net/1721.1/30577
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

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