# Conditional probabilities via line arrangements and point configurations

@article{Clarke2020ConditionalPV, title={Conditional probabilities via line arrangements and point configurations}, author={Oliver Clarke and Fatemeh Mohammadi and Harshit J. Motwani}, journal={arXiv: Commutative Algebra}, year={2020} }

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…

## 3 Citations

Incidence geometry in the projective plane via almost-principal minors of symmetric matrices

- Mathematics, Computer ScienceArXiv
- 2021

It is proved that the implication problem for Gaussian CI is polynomial-time equivalent to the existential theory of the reals, and two complexity results about Gaussian conditional independence structures are proved.

Generalized Cohen-Macaulay binomial edge ideals

- Mathematics
- 2021

Let G be a simple graph on n vertices and let JG,m be the generalized binomial edge ideal associated to G in the polynomial ring K[xij, 1 ≤ i ≤ m, 1 ≤ j ≤ n]. We classify the Cohen-Macaulay…

Matroid stratifications of hypergraph varieties, their realization spaces, and discrete conditional independence models

- Mathematics
- 2021

We study conditional independence (CI) models in statistical theory, in the case of discrete random variables, from the point of view of algebraic geometry and matroid theory. Any CI model with…

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