0

For a matrix $X\in\mathbb{R}^{d\times n}$, what condition can I impose on $X$ to make the collection of its columns generic in the sense that they look like the result of uniformly sampling a convex region in $\mathbb{R}^d$? Ideas or relevant papers are welcome and appreciated. Thanks.

Min Wu
  • 461
  • So, the question is on uniformly sampling a convex region, right? – Rodrigo de Azevedo Oct 26 '19 at 05:55
  • No, the question is on "what conditions I can impose on X" to make its columns look like uniform point cloud on a convex region. – Min Wu Oct 26 '19 at 05:58
  • 1
    Why make it look like the original if you can get the original? – Rodrigo de Azevedo Oct 26 '19 at 06:28
  • You want something like a likelihood measure, that given $X$ will tell you how "likely" it is to come from a uniform sampling on a convex? As it is, it is unclear what you are asking. Any distribution of points may come from such a sampling, although possibly with a low likelihood. – Federico Poloni Oct 26 '19 at 08:23
  • Sorry for the confusions. I will restate the problem again. – Min Wu Oct 26 '19 at 16:46
  • Possibly related: https://mathoverflow.net/q/9854/91764 and https://mathoverflow.net/q/164043/91764 and https://mathoverflow.net/q/243687/91764 – Rodrigo de Azevedo Oct 26 '19 at 22:00

0 Answers0