Completion problems, of recovering points from a set of observed coordinates, are abundant in applications to image reconstruction, phylogenetics, and data science. We consider a completion problem coming from algebraic statistics, of determining those observed probabilities which can be finitely completed to a probability distribution in a given log--linear model. These observed probabilities either have a unique completion or two completions to the log--linear model depending on the set of observed coordinates.

翻译：完备化问题——从一组观测坐标恢复未知点——在图像重建、系统发育学和数据科学等应用中广泛存在。本文考虑一个来自代数统计的完备化问题：确定那些能够被有限完备化为给定对数线性模型中概率分布的观测概率。根据观测坐标集合的不同，这些观测概率要么存在唯一完备化结果，要么有两种完备化结果使之符合对数线性模型。