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Sanjoy Dasgupta
University of California San Diego
A Central Limit Theorem for Projections
May 8, 2006 12:00pm
Abstract:
Suppose the random variable $X \in \R^D$ 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.
This is joint work with Daniel Hsu and Nakul Verma.
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