Random Points on an Algebraic Manifold
Abstract
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic manifolds. This method is based on intersecting with random linear spaces. It produces independent and identically distributed samples, works in the presence of multiple connected components, and is simple to implement. We present applications to computational statistical physics and topological data analysis.
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Information & Authors
Information
Published In
SIAM Journal on Mathematics of Data Science
Pages: 683 - 704
DOI: 10.1137/19M1271178
ISSN (online): 2577-0187
Copyright
© 2020, Society for Industrial and Applied Mathematics.
History
Submitted: 28 June 2019
Accepted: 29 May 2020
Published online: 24 August 2020
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Funding Information
H2020 European Research Council https://doi.org/10.13039/100010663 : 787840
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