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## Asymptotics of Gaussian Regularized Least-Squares

### 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

Topics: AI, machine learning, regularization
Year: 2005
OAI identifier: oai:dspace.mit.edu:1721.1/30577
Provided by: DSpace@MIT