论文标题
几乎紧密的绑定，用于将椭圆形安装到高斯随机点上
A Nearly Tight Bound for Fitting an Ellipsoid to Gaussian Random Points
论文作者
论文摘要
我们证明，对于$ c> 0 $，一个足够小的通用常数，一组随机的$ c d^2/\ log^4（d）$独立的高斯随机点在$ \ mathbb {r}^d $中躺在具有很高可能性的常见椭圆形上。这几乎建立了对数因素内的〜\ cite {saundersoncpw12}的猜想。在过去的十年中，后者的猜想引起了人们的重大关注，因为它与机器学习和方案总和下限的连接有关某些统计问题。
We prove that for $c>0$ a sufficiently small universal constant that a random set of $c d^2/\log^4(d)$ independent Gaussian random points in $\mathbb{R}^d$ lie on a common ellipsoid with high probability. This nearly establishes a conjecture of~\cite{SaundersonCPW12}, within logarithmic factors. The latter conjecture has attracted significant attention over the past decade, due to its connections to machine learning and sum-of-squares lower bounds for certain statistical problems.
