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Citation bot (talk | contribs) Alter: template type. Add: eprint, class, authors 1-1. Removed proxy/dead URL that duplicated identifier. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Headbomb | Linked from Wikipedia:WikiProject_Academic_Journals/Journals_cited_by_Wikipedia/Sandbox | #UCB_webform_linked 35/41 |
→Fourier random features: the Fourier transform of the kernel has the inverse variance |
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One way to construct such a ''z'' is to randomly sample from the [[Fourier transformation]] of the kernel<ref>{{Cite journal |last1=Rahimi |first1=Ali |last2=Recht |first2=Benjamin |date=2007 |title=Random Features for Large-Scale Kernel Machines |url=https://proceedings.neurips.cc/paper/2007/hash/013a006f03dbc5392effeb8f18fda755-Abstract.html |journal=Advances in Neural Information Processing Systems |publisher=Curran Associates, Inc. |volume=20}}</ref><math display="block">\varphi(x) = \frac{1}{\sqrt D}[\cos\langle w_1, x\rangle, \sin\langle w_1, x\rangle, \cdots \cos\langle w_D, x\rangle, \sin\langle w_D, x\rangle]^T</math>where <math>w_1, ..., w_D</math> are independent samples from the normal distribution <math>N(0, \sigma^{-2} I)</math>.
'''Theorem:''' <math>\mathbb E[\langle \varphi(x), \varphi(y)\rangle] = e^{\frac{\|x-y\|^2}{2\sigma^2}}</math>.
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