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Large deviation principles induced by the Stiefel manifold, and random multi-dimensional projections
Autor:
Kim, Steven Soojin, Ramanan, Kavita
Given an $n$-dimensional random vector $X^{(n)}$ , for $k < n$, consider its $k$-dimensional projection $\mathbf{a}_{n,k}X^{(n)}$, where $\mathbf{a}_{n,k}$ is an $n \times k$-dimensional matrix belonging to the Stiefel manifold $\mathbb{V}_{n,k}$ of
Externí odkaz:
http://arxiv.org/abs/2105.04685
Consider the projection of an $n$-dimensional random vector onto a random $k_n$-dimensional basis, $k_n \leq n$, drawn uniformly from the Haar measure on the Stiefel manifold of orthonormal $k_n$-frames in $\mathbb{R}^n$, in three different asymptoti
Externí odkaz:
http://arxiv.org/abs/1912.13447
Publikováno v:
In Advances in Applied Mathematics March 2022 134
Let $p\in[1,\infty]$. Consider the projection of a uniform random vector from a suitably normalized $\ell^p$ ball in $\mathbb{R}^n$ onto an independent random vector from the unit sphere. We show that sequences of such random projections, when suitab
Externí odkaz:
http://arxiv.org/abs/1512.04988
Autor:
Kim, Steven Soojin, Ramanan, Kavita
The study of high-dimensional distributions is of interest in probability theory, statistics and asymptotic convex geometry, where the object of interest is the uniform distribution on a convex set in high dimensions. The $\ell^p$ spaces and norms ar
Externí odkaz:
http://arxiv.org/abs/1509.05442
The empirical mean of $n$ independent and identically distributed (i.i.d.) random variables $(X_1,\dots,X_n)$ can be viewed as a suitably normalized scalar projection of the $n$-dimensional random vector $X^{(n)}\doteq(X_1,\dots,X_n)$ in the directio
Externí odkaz:
http://arxiv.org/abs/1508.04402
Publikováno v:
The Annals of Probability, 2017 Nov 01. 45(6B), 4419-4476.
Externí odkaz:
https://www.jstor.org/stable/26362274
Akademický článek
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Publikováno v:
Advances in the Mathematical Sciences; 2016, p253-270, 18p