Staged trees are a recently-developed, powerful family of probabilistic graphical models. An equivalence class of staged trees has now been characterised, and two fundamental statistical operators have been defined to traverse the equivalence class of a given staged tree. Here, two staged trees are said to be statistically equivalent when they represent the same set of distributions. Probabilistic graphical models such as staged trees are increasingly being used for causal analyses. Staged trees which are within the same equivalence class can encode very different causal hypotheses but data alone cannot help us distinguish between these. Therefore, in using score-based methods to learn the model structure and distributions from data for causal analyses, we should expect that a suitable scoring function is one which assigns the same score to statistically equivalent models. No scoring function has yet been proven to have this desirable property for staged trees. In this paper, we present a novel Bayesian Dirichlet scoring function based on path uniformity and mass conversation, and prove that this new scoring function is score-equivalent for staged trees.
翻译:阶梯树是最近开发的、 强大的概率图形模型组合。 已经对分层树的等效类进行了定性, 并定义了两个基本的统计操作员来绕过某一分层树的等效类。 这里, 两种分层树代表同一组分布, 据说在统计上是等效的。 象分层树这样的概率图形模型正越来越多地用于因果关系分析。 同一等级的分层树可以对非常不同的因果关系假设进行编码, 但数据本身无法帮助我们区分这些假设。 因此, 在使用分级法从因果关系分析的数据中学习模型结构和分布时, 我们应该期望一个合适的评分函数是给同级的等值模型。 还没有证明任何评分功能对分树具有这种可取的属性。 在本文中, 我们根据路径的统一性和大众对话, 展示了一个新的巴耶斯德利特评分功能, 并且证明这个新的评分函数是对分的等值。