We classify the two-way quasi-independence models (independence models with structural zeros) that have rational maximum likelihood estimators, or MLEs. We give a necessary and sufficient condition on the bipartite graph associated to the model for the MLE to be rational. In this case, we give an explicit formula for the MLE in terms of combinatorial features of this graph. We also use the Horn uniformization to show that for general log-linear models $\mathcal{M}$ with rational MLE, any model obtained by restricting to a face of the cone of sufficient statistics of $\mathcal{M}$ also has rational MLE.

中文翻译：

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有理最大似然估计的拟独立模型

我们对具有合理最大似然估计量或MLE的双向准独立模型（具有结构零点的独立模型）进行分类。我们在与模型相关的二部图上给出了一个必要和充分的条件，以使MLE变得合理。在这种情况下，我们根据该图的组合特征给出了MLE的明确公式。我们还使用Horn均匀化来表明对于一般对数线性模型$\mathcal{中号}$ 如果使用有理MLE，则通过限制圆锥的足够统计量的面而获得的任何模型 $\mathcal{中号}$ 也有合理的MLE。