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.

Keywords

  1. sampling
  2. approximating integrals
  3. geometrical probability
  4. algebraic geometry
  5. statistical physics
  6. topological data analysis

MSC codes

  1. 60B05
  2. 62D05
  3. 51H30

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Information & Authors

Information

Published In

cover image SIAM Journal on Mathematics of Data Science
SIAM Journal on Mathematics of Data Science
Pages: 683 - 704
ISSN (online): 2577-0187

History

Submitted: 28 June 2019
Accepted: 29 May 2020
Published online: 24 August 2020

Keywords

  1. sampling
  2. approximating integrals
  3. geometrical probability
  4. algebraic geometry
  5. statistical physics
  6. topological data analysis

MSC codes

  1. 60B05
  2. 62D05
  3. 51H30

Authors

Affiliations

Funding Information

H2020 European Research Council https://doi.org/10.13039/100010663 : 787840

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