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

@inproceedings{Clarke2021MatroidSO, title={Matroid stratifications of hypergraph varieties, their realization spaces, and discrete conditional independence models}, author={Oliver Clarke and Kevin Grace and Fatemeh Mohammadi and Harshit J. Motwani}, year={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 hidden random variables corresponds to a variety defined by certain determinantal conditions on a matrix whose entries are probabilities of events involving the observed random variables. We show that any CI variety, and more generally any hypergraph variety, admits a matroid stratification. Our main…

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