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arXiv · 2505.02404

Decomposing conditional independence ideals with hidden variables

Yulia Alexandr·Kristen Dawson·Hannah Friedman·Fatemeh Mohammadi·Pardis Semnani·Teresa Yu
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Abstract

We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models, we show that this is a decomposition into radical ideals by displaying Gr\"obner bases for the components. We identify conditions under which the components are prime, and establish formulas for the dimensions of these prime ideals. Moreover, we show that the components in the decomposition can be grouped into equivalence classes defined by their combinatorial structure, and we derive a closed formula for the number of such classes.

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Yulia Alexandr, Kristen Dawson, Hannah Friedman, Fatemeh Mohammadi, Pardis Semnani, Teresa Yu. 2025-05-05. Decomposing conditional independence ideals with hidden variables. https://arxiv.org/abs/2505.02404

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