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A concentration theorem for projections
Sanjoy Dasgupta, Daniel Hsu, Nakul Verma
Abstract:
$X in R^D$ has mean zero and finite second moments. We show that there is a precise sense in which almost all linear projections of $X$ into $R^d$ (for $d < D$) look like a scale-mixture of spherical Gaussians -- specifically, a mixture of distributions $N(0, sigma^2 I_d)$ where the weight of the particular $sigma$ component is $P (| X |^2 = sigma^2 D)$. The extent of this effect depends upon the ratio of $d$ to $D$, and upon a particular coefficient of eccentricity of $X$'s distribution. We explore this result in a variety of experiments.
Keywords:
Pages: 114-121
PS Link:
PDF Link: /papers/06/p114-dasgupta.pdf
BibTex:
@INPROCEEDINGS{Dasgupta06,
AUTHOR = "Sanjoy Dasgupta
and Daniel Hsu and Nakul Verma",
TITLE = "A concentration theorem for projections",
BOOKTITLE = "Proceedings of the Proceedings of the Twenty-Second Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2006",
PAGES = "114-121"
}
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