An O(n) algorithm for generating uniform random vectors in n-dimensional cones

Arun I.; Murugesan Venkatapathi

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arXiv · 2101.00936

An O(n) algorithm for generating uniform random vectors in n-dimensional cones

Arun I.·Murugesan Venkatapathi

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Abstract

Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random vectors in its subspaces typically involves the inefficiency of rejecting vectors falling outside, or re-weighting a non-uniformly distributed set of samples. Both approaches become severely ineffective as n increases. We present an efficient algorithm to generate uniformly distributed random directions in n-dimensional cones, to aid searching and sampling tasks in high dimensions.

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Arun I., Murugesan Venkatapathi. 2021-01-04. An O(n) algorithm for generating uniform random vectors in n-dimensional cones. https://arxiv.org/abs/2101.00936

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