Conditional probabilities via line arrangements and point configurations

  title={Conditional probabilities via line arrangements and point configurations},
  author={Oliver Clarke and Fatemeh Mohammadi and Harshit J. Motwani},
  journal={arXiv: Commutative Algebra},
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal whose algebraic invariants are encoded in a hypergraph. The primary decompositions of these ideals give a characterisation of the distributions satisfying the original CI statements. Classically, these ideals are generated by 2-minors of a matrix of variables… 

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