Conditional probabilities via line arrangements and point configurations Ghent University
We study the connection between probability distributions satisfying certain condi- tional 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 distribu- tions satisfying the original CI statements. Classically, these ideals ...