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arXiv · 1306.5829

A Cubic Algorithm for Computing Gaussian Volume

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.

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Ben Cousins, Santosh Vempala. 2013-06-25. A Cubic Algorithm for Computing Gaussian Volume. https://arxiv.org/abs/1306.5829

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