Algebraic geometry of Bayesian networks

Authors:
Luis David Garcia;Michael Stillman;Bernd Sturmfels
Affiliations:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA;Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA;Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA
Venue:
Journal of Symbolic Computation
Year:
2005

Citing 4
Cited 3

Probabilistic reasoning in intelligent systems: networks of plausible inference

Probabilistic reasoning in intelligent systems: networks of plausible inference
Localization and primary decomposition of polynomial ideals

Journal of Symbolic Computation
Conditional Independences among Four Random Variables III: Final Conclusion

Combinatorics, Probability and Computing
On the geometry of Bayesian graphical models with hidden variables

UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence

Algebraic statistics in model selection

UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Resultants in genetic linkage analysis

Journal of Symbolic Computation
Multigraded commutative algebra of graph decompositions

Journal of Algebraic Combinatorics: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties.