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 scalemixture 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: 114121
PS Link:
PDF Link: /papers/06/p114dasgupta.pdf
BibTex:
@INPROCEEDINGS{Dasgupta06,
AUTHOR = "Sanjoy Dasgupta
and Daniel Hsu and Nakul Verma",
TITLE = "A concentration theorem for projections",
BOOKTITLE = "Proceedings of the TwentySecond Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI06)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2006",
PAGES = "114121"
}

