June 6, 2024, 4:44 a.m. | Andrea Montanari, Kangjie Zhou

cs.LG updates on arXiv.org arxiv.org

arXiv:2406.02970v1 Announce Type: cross
Abstract: Given $d$-dimensional standard Gaussian vectors $\boldsymbol{x}_1,\dots, \boldsymbol{x}_n$, we consider the set of all empirical distributions of its $m$-dimensional projections, for $m$ a fixed constant. Diaconis and Freedman (1984) proved that, if $n/d\to \infty$, all such distributions converge to the standard Gaussian distribution. In contrast, we study the proportional asymptotics, whereby $n,d\to \infty$ with $n/d\to \alpha \in (0, \infty)$. In this case, the projection of the data points along a typical random subspace is again Gaussian, …

abstract arxiv cloud converge cs.lg found low math.oc math.pr polynomial set standard type vectors

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