A Concentration Theorem for Projections
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.
Cite
Text
Dasgupta et al. "A Concentration Theorem for Projections." Conference on Uncertainty in Artificial Intelligence, 2006.Markdown
[Dasgupta et al. "A Concentration Theorem for Projections." Conference on Uncertainty in Artificial Intelligence, 2006.](https://mlanthology.org/uai/2006/dasgupta2006uai-concentration/)BibTeX
@inproceedings{dasgupta2006uai-concentration,
title = {{A Concentration Theorem for Projections}},
author = {Dasgupta, Sanjoy and Hsu, Daniel J. and Verma, Nakul},
booktitle = {Conference on Uncertainty in Artificial Intelligence},
year = {2006},
url = {https://mlanthology.org/uai/2006/dasgupta2006uai-concentration/}
}