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.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/30577 |
| Date | 20 October 2005 |
| Creators | Lippert, Ross, Rifkin, Ryan |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Format | 1 p., 7286963 bytes, 527607 bytes, application/postscript, application/pdf |
| Relation | Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory |
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