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.

本论文研究了树状结构因果模型的识别问题，提出了一个随机多项式时间算法来判断结构参数的识别性，并给出了相应参数的分数亚方根多项式表达式。