A concentration theorem for projections
Machine Learning
2012-07-02 v1 Machine Learning
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
@article{arxiv.1206.6813,
title = {A concentration theorem for projections},
author = {Sanjoy Dasgupta and Daniel Hsu and Nakul Verma},
journal= {arXiv preprint arXiv:1206.6813},
year = {2012}
}
Comments
Appears in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (UAI2006)