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The Geometry of Causal Probability Trees that are Algebraically Constrained

In: Optimal Design and Related Areas in Optimization and Statistics

Author

Listed:
  • E. Riccomagno

    (Università degli Studi di Genova)

  • J. Q. Smith

    (The University of Warwick)

Abstract

Summary Algebraic geometry is used to study properties of a class of discrete distributions defined on trees and called algebraically constrained statistical models. This structure has advantages in studying marginal models as it is closed under learning marginal mass functions. Furthermore, it allows a more expressive and general definition of causal relationships and probabilistic hypotheses than some of those currently in use. Simple examples show the flexibility and expressiveness of this model class which generalizes discrete Bayes networks.

Suggested Citation

  • E. Riccomagno & J. Q. Smith, 2009. "The Geometry of Causal Probability Trees that are Algebraically Constrained," Springer Optimization and Its Applications, in: Luc Pronzato & Anatoly Zhigljavsky (ed.), Optimal Design and Related Areas in Optimization and Statistics, chapter 6, pages 133-154, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-79936-0_6
    DOI: 10.1007/978-0-387-79936-0_6
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