Timeline for Uniform sampling from general simplex with a twist
Current License: CC BY-SA 3.0
5 events
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Nov 10, 2018 at 23:59 | comment | added | Sasho Nikolov | @Rzu Any polytope is a (possibly singular) linear transformation of the probability simplex. Sampling from an arbitrary polytope given by its vertices is more complicated, I believe, and probably needs the full power of Monte Carlo methods. But in this case, I don't see why you say that the linear transformation is singular. | |
| Nov 9, 2018 at 13:56 | comment | added | R zu | @SashoNikolov Is it ok if multiple $a_i$ are zero? In that case, the transformation from the standard simplex to non-standard simplex is linear and singular. Projection of a uniform distribution of points over an equilateral triangle to the base would give a non-uniform distribution of points on the base. The center of the base will have more points. | |
| Jul 14, 2016 at 0:32 | comment | added | Sasho Nikolov | These algorithms are quite the overkill for the problem. Sampling from any simplex $\Delta$ reduces to sampling from the probability simplex as long as you can identify the vertices of $\Delta$. Identifying the vertices in this case is an exercise. There are a number of (simple) classical algorithms for sampling from the probability simplex. | |
| Jul 5, 2016 at 2:30 | history | answered | john mangual | CC BY-SA 3.0 |