# Conditional independence ideals with hidden variables

@article{Clarke2020ConditionalII, title={Conditional independence ideals with hidden variables}, author={Oliver Clarke and Fatemeh Mohammadi and Johannes Rauh}, journal={Adv. Appl. Math.}, year={2020}, volume={117}, pages={102029} }

We study a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables. Such CI statements correspond to determinantal conditions on a matrix whose entries are probabilities of events involving the observed random variables. We focus on an example that generalizes the CI ideals of the intersection axiom. In this example, the minimal primes are again determinantal ideals, which is not true in general.

## 3 Citations

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The method is based on the algorithm for primary decomposition by Gianni, Trager and Zacharias, but it was not able to decompose the ideal using the standard form of that algorithm, nor by any other method known to us.

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