The space of compatible full conditionals is a unimodular toric variety

Aleksandra B. Slavkovic, Seth Sullivant

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The set of all m-tuples of compatible full conditional distributions on discrete random variables is an algebraic set whose defining ideal is a unimodular toric ideal. We identify the defining polynomials of these ideals with closed walks on a bipartite graph. Our algebraic characterization provides a natural generalization of the requirement that compatible conditionals have identical odds ratios and holds regardless of the patterns of zeros in the conditional arrays.

Original languageEnglish (US)
Pages (from-to)196-209
Number of pages14
JournalJournal of Symbolic Computation
Volume41
Issue number2
DOIs
StatePublished - Feb 1 2006

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Toric Varieties
Random variables
Polynomials
Toric Ideal
Discrete random variable
Algebraic Set
Odds Ratio
Conditional Distribution
Walk
Bipartite Graph
Closed
Polynomial
Requirements
Zero
Generalization

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics

Cite this

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The space of compatible full conditionals is a unimodular toric variety. / Slavkovic, Aleksandra B.; Sullivant, Seth.

In: Journal of Symbolic Computation, Vol. 41, No. 2, 01.02.2006, p. 196-209.

Research output: Contribution to journalArticle

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