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.

中文翻译：

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具有隐藏变量的条件独立理想

我们研究了一类与带有隐藏变量的条件独立 (CI) 语句相关的行列式理想。这种 CI 语句对应于矩阵上的行列式条件，其条目是涉及观察到的随机变量的事件的概率。我们关注一个概括了交集公理的 CI 理想的例子。在这个例子中，最小素数再次是行列式理想，这在一般情况下是不正确的。