Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic computation. However, standard approaches based on Gröbner bases become computationally infeasible beyond small settings due to their doubly exponential complexity. In this work, we study how to practically use symbolic computation for deciding rational identifiability. In particular, we present an efficient algorithm that provably finds the lowest degree identifying formulas. For a causal effect of interest, if there exists an identification formula of a prespecified maximal degree, our algorithm returns such a formula in quasi-polynomial time.

翻译：在潜变量混杂下从观测数据中确定因果效应的可识别性是因果推断的核心挑战之一。对于线性结构因果模型，因果效应的可识别性可通过符号计算判定。然而，基于格罗布纳基的标准方法因其双重指数复杂度，在超出小规模场景后变得计算上不可行。本文研究如何在实际中运用符号计算确定有理可识别性，特别地，我们提出一种高效算法，该算法可证明能够找到最低阶次的识别公式。若存在具有预设最高阶次的识别公式，我们的算法将在拟多项式时间内返回此类公式。