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.
THE GEOMETRY OF CAUSAL PROBABILITY TREES THAT ARE ALGEBRAICALLY CONSTRAINED
RICCOMAGNO, EVA;
2009-01-01
Abstract
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.
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