A cubic algorithm for computing gaussian volume
SODA(2014)
摘要
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 the integration algorithm is O*(n3) while the complexity of the sampling algorithm is O*(n3) for the first sample and O*(n2) 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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关键词
algorithms,design,complexity measures and classes,general,theory,geometrical problems and computations
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