We study the maximum likelihood (ML) degree of discrete exponential independence models and models defined by the second hypersimplex. For models with two independent variables, we show that the ML degree is an invariant of a matroid associated to the model. We use this description to explore ML degrees via hyperplane arrangements. For independence models with more variables, we investigate the connection between the vanishing of factors of its principal $A$-determinant and its ML degree. Similarly, for models defined by the second hypersimplex, we determine its principal $A$-determinant and give computational evidence towards a conjectured lower bound of its ML degree.

翻译：我们研究离散指数独立模型与由第二超单形定义的模型的最大似然（ML）度。对于具有两个独立变量的模型，我们证明ML度是与该模型相关联的拟阵的不变量。我们利用这一描述通过超平面排列探索ML度。对于变量更多的独立模型，我们研究其主$A$-行列式因子消失与ML度之间的联系。类似地，对于由第二超单形定义的模型，我们确定其主$A$-行列式，并提供计算证据以支持关于其ML度的一个猜想下界。