Conditional Independence Ideals with Hidden Variables
- Oliver Clarke (University of Bristol, Bristol, United Kingdom)
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 flattenings of marginals of the tensor P of joint probabilities of 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.