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Jan
13
awarded  Nice Question
Jan
3
comment Computation complexity of calculating the cdf of an n-th dimensional gaussian random vector
essentially needs to know a point inside the convex set to "get started". Since your set is an explicitly given intersection of n halfspaces, it should be straightforward to explicitly obtain such a point. In other words, I feel that it should be possible to work around the requirement and apply the Cousins-Vempala paper to your setting.
Jan
3
comment Computation complexity of calculating the cdf of an n-th dimensional gaussian random vector
Ah, good question. Okay, it occurs to me now that for relative accuracy $\epsilon$ you should be able to do it in time $\mathrm{poly}(n/\epsilon)$ using this paper of Cousins and Vempala (or those that it cites): arxiv.org/abs/1306.5829 It gives such an approximation for the Gaussian volume of any convex set, in fact. A small catch is that it requires some technical condition like the set containing the unit ball. However, from what I know of this subject, that is not a very strict requirement. It's more like a simple example of a possible requirement; really, the algorithm just
Jan
3
answered Computation complexity of calculating the cdf of an n-th dimensional gaussian random vector
Nov
27
awarded  Citizen Patrol
Nov
13
answered Cardinality of intersection of a random subset with a fixed subset
Oct
26
awarded  Enthusiast
Oct
22
accepted What are good English-language sources for reading about the Luzin affair?
Oct
19
awarded  Informed
Oct
19
comment Convergence of orthogonal polynomial expansions
Oh, I guess the desired uniform convergence statement from in #1 probably follows from Egorov's theorem.
Oct
19
answered Convergence of orthogonal polynomial expansions
Oct
18
awarded  Yearling
Oct
14
asked What are good English-language sources for reading about the Luzin affair?
Oct
8
awarded  Constituent
Oct
3
awarded  Quorum
Oct
3
awarded  Caucus
Oct
1
answered For interior point methods of linear programming, what is the “L” in the computational complexity $\mathcal{O}(n^3 L)$?
Sep
18
comment point in polytope
@Igor: en.wikipedia.org/wiki/Convex_position
Jul
20
answered Video lectures of mathematics courses available online for free
Jul
18
comment Multivariate Central Limit Theorem For Non-Identical Distribution
I kind of agree with the (now-deleted) comment made by OP that it's not clear why this question is On Hold. It's not so easy to find clear statements about the multidimensional, non-iid, CLT in the literature. For example, the (first?) paper on the multidim CLT by Sazonov only treats the iid case, and the standard textbook by Bhattacharya and Rao is a bit of a nightmare to read (in my opinion).