Algebraic geometry of discrete interventional models
Abstract
We investigate the algebra and geometry of general interventions in discrete DAG models. To this end, we introduce a theory for modeling soft interventions in the more general family of staged tree models and develop the formalism to study these models as parametrized subvarieties of a product of probability simplices. We then consider the problem of finding their defining equations, and we derive a combinatorial criterion for identifying interventional staged tree models for which the defining ideal is toric. We apply these results to the class of discrete interventional DAG models and establish a criteria to determine when these models are toric varieties.
Keywords
Cite
@article{arxiv.2012.03593,
title = {Algebraic geometry of discrete interventional models},
author = {Eliana Duarte and Liam Solus},
journal= {arXiv preprint arXiv:2012.03593},
year = {2023}
}
Comments
This version includes some minors revision to examples, intro and statistical/algebraic outlook