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• W3096434783 abstract "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, however, in the presence of hidden variables, they contain higher degree minors. This leads to the study of the structure of determinantal hypergraph ideals whose decompositions can be understood in terms of point and line configurations in the projective space." @default.
• W3096434783 created "2020-11-09" @default.
• W3096434783 creator A5041824598 @default.
• W3096434783 creator A5046511507 @default.
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• W3096434783 date "2020-11-04" @default.
• W3096434783 modified "2023-09-27" @default.
• W3096434783 title "Conditional probabilities via line arrangements and point configurations." @default.
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• W3096434783 hasPublicationYear "2020" @default.
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