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Computer Science > Data Structures and Algorithms

arXiv:1306.5829 (cs)
[Submitted on 25 Jun 2013 (v1), last revised 11 Jul 2013 (this version, v2)]

Title:A Cubic Algorithm for Computing Gaussian Volume

Authors:Ben Cousins, Santosh Vempala
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Abstract:We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of integration is $O^*(n^3)$ while the complexity of sampling is $O^*(n^3)$ for the first sample and $O^*(n^2)$ for every subsequent sample. These bounds improve on the corresponding state-of-the-art by a factor of $n$. Our improvement comes from several aspects: better isoperimetry, smoother annealing, avoiding transformation to isotropic position and the use of the "speedy walk" in the analysis.
Comments: 23 pages
Subjects: Data Structures and Algorithms (cs.DS); Functional Analysis (math.FA); Probability (math.PR)
Cite as: arXiv:1306.5829 [cs.DS]
  (or arXiv:1306.5829v2 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.1306.5829

Submission history

From: Ben Cousins [view email]
[v1] Tue, 25 Jun 2013 02:04:58 UTC (19 KB)
[v2] Thu, 11 Jul 2013 05:35:52 UTC (21 KB)
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