An $$\mathcal {O}$$ O (n) Algorithm for Generating Uniform Random Vectors in n-dimensional Cones

Arun I. and Murugesan Venkatapathi ()
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Arun I.: Indian Institute of Science
Murugesan Venkatapathi: Indian Institute of Science

Sankhya A: The Indian Journal of Statistics, 2025, vol. 87, issue 2, No 3, 327-348

Abstract: Abstract Random vectors distributed uniformly in the direction space are widely used, and the computational cost of generating a vector in n dimensions 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 sampling, searching and optimization tasks in high dimensions.

Keywords: High dimensions; spherical cap; random search; Monte Carlo; Primary 62-08; Secondary 68W20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13171-025-00387-9

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