Additive noise models (ANMs) are an important setting studied in causal inference. Most of the existing works on ANMs assume causal sufficiency, i.e., there are no unobserved confounders. This paper focuses on confounded ANMs, where a set of treatment variables and a target variable are affected by an unobserved confounder that follows a multivariate Gaussian distribution. We introduce a novel approach for estimating the average causal effects (ACEs) of any subset of the treatment variables on the outcome and demonstrate that a small set of interventional distributions is sufficient to estimate all of them. In addition, we propose a randomized algorithm that further reduces the number of required interventions to poly-logarithmic in the number of nodes. Finally, we demonstrate that these interventions are also sufficient to recover the causal structure between the observed variables. This establishes that a poly-logarithmic number of interventions is sufficient to infer the causal effects of any subset of treatments on the outcome in confounded ANMs with high probability, even when the causal structure between treatments is unknown. The simulation results indicate that our method can accurately estimate all ACEs in the finite-sample regime. We also demonstrate the practical significance of our algorithm by evaluating it on semi-synthetic data.

翻译：加性噪声模型（ANM）是因果推断研究中的一个重要设定。现有关于ANM的研究大多假设因果充分性，即不存在未观测混杂因子。本文聚焦于混杂ANM，其中一组处理变量与目标变量受到服从多元高斯分布的未观测混杂因子影响。我们提出了一种估计任意处理变量子集对结果变量的平均因果效应（ACE）的新方法，并证明仅需少量干预分布即可估计所有效应。此外，我们提出一种随机化算法，将所需干预次数进一步降低至节点数的多对数级别。最后，我们证明这些干预同样足以恢复观测变量间的因果结构。这表明即使处理变量间的因果结构未知，在多对数级别的干预次数下仍能以高概率推断混杂ANM中任意处理子集对结果的因果效应。仿真结果表明我们的方法在有限样本条件下能准确估计所有ACE。我们还在半合成数据上评估算法，验证了其实际应用价值。