Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that would otherwise be untestable due to the unobserved variables and can be used to constrain estimation procedures to improve statistical efficiency. Knowing the complete set of observable constraints is thus ideal, but this can be difficult to determine in many settings. In models with categorical observed variables and a joint distribution that is completely characterized by linear relations to the unobservable response function variables, we develop a systematic method for deriving the complete set of observable constraints. We illustrate the method in several new settings, including ones that imply both inequality and equality constraints.

翻译：隐变量图模型有时会蕴含比简单条件独立性关系更为复杂的可观测分布约束。这些可观测约束能够证伪模型中的假设——这些假设若仅因变量未观测而无法检验——并可用于约束估计过程以提高统计效率。因此，获知可观测约束的完整集合是最理想的情况，但在许多场景中这往往难以确定。针对具有分类观测变量且联合分布完全由与不可观测响应函数变量的线性关系所刻画的模型，我们提出了一种系统化方法来推导可观测约束的完整集合。我们在若干新场景中演示了该方法的应用，包括同时蕴含不等式约束与等式约束的情形。