This paper focuses on the computational complexity of computing empirical plug-in estimates for causal effect queries. Given a causal graph and observational data, any identifiable causal query can be estimated from an expression over the observed variables, called the estimand. The estimand can then be evaluated by plugging in probabilities computed empirically from data. In contrast to conventional wisdom, which assumes that high dimensional probabilistic functions will lead to exponential evaluation time of the estimand. We show that computation can be done efficiently, potentially in time linear in the data size, depending on the estimand's hypergraph. In particular, we show that both the treewidth and hypertree width of the estimand's structure bound the evaluation complexity of the plug-in estimands, analogous to their role in the complexity of probabilistic inference in graphical models. Often, the hypertree width provides a more effective bound, since the empirical distributions are sparse.

翻译：本文聚焦于计算因果效应查询的经验插件估计的计算复杂度。给定因果图与观测数据，任何可识别的因果查询均可通过观测变量的表达式（称为估计量）进行估计。随后，可通过将数据经验计算得到的概率代入该估计量进行评估。与传统观点认为高维概率函数将导致估计量评估时间呈指数增长不同，本文证明计算过程可以高效完成，其时间复杂度可能随数据规模线性增长，具体取决于估计量的超图结构。特别地，我们证明估计量结构的树宽与超树宽共同限定了插件估计量的评估复杂度，这与它们在概率图模型推理复杂度中的作用相类似。由于经验分布具有稀疏性，超树宽通常能提供更有效的复杂度边界。