Linear structural causal models (SCMs) are used to express and analyse the relationships between random variables. Direct causal effects are represented as directed edges and confounding factors as bidirected edges. Identifying the causal parameters from correlations between the nodes is an open problem in artificial intelligence. In this paper, we study SCMs whose directed component forms a tree. Van der Zander et al. (AISTATS'22, PLMR 151, pp. 6770--6792, 2022) give a PSPACE-algorithm for the identification problem in this case, which is a significant improvement over the general Gr\"obner basis approach, which has doubly-exponential time complexity in the number of structural parameters. In this work, we present a randomized polynomial-time algorithm, which solves the identification problem for tree-shaped SCMs. For every structural parameter, our algorithms decides whether it is generically identifiable, generically 2-identifiable, or generically unidentifiable. (No other cases can occur.) In the first two cases, it provides one or two fractional affine square root terms of polynomials (FASTPs) for the corresponding parameter, respectively.

翻译：线性结构因果模型（SCMs）用于表达和分析随机变量之间的关系。直接因果效应表示为有向边，混杂因子表示为双向边。从节点间的相关性辨识因果参数是人工智能领域的一个开放性问题。本文研究有向分量构成树的SCMs。Van der Zander等人（AISTATS'22, PLMR 151, pp. 6770--6792, 2022）针对该情形给出了一个辨识问题的PSPACE算法，相比结构参数数量上具有双指数时间复杂度的通用Gröbner基方法，这是显著改进。本文提出一个随机多项式时间算法，可解决树形SCMs的辨识问题。对于每个结构参数，该算法判定其是否为一般可辨识、一般2-可辨识或一般不可辨识（不存在其他情形）。在前两种情形中，算法分别提供对应参数的一个或两个多项式分数仿射平方根项（FASTPs）。