Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.

翻译：因果效应估计在仅有观测数据的情况下已被众多研究者探讨。针对可识别的因果查询，已有完备的逐点估计算法；对于不可识别的因果查询，研究者开发了多项式规划方法以估计因果效应的紧致界。然而，当变量支撑集规模较大时，这些方法在计算上难以优化。本文分析了“弱混杂”对因果估计量的影响。具体而言，假设导致查询不可识别的未观测混杂变量的熵较小，我们提出了一种高效线性规划方法以推导因果效应的上下界。我们证明该界限具有一致性：当未观测混杂变量的熵趋近于零时，上下界之间的差距亦趋近于零。最后，通过合成数据与真实数据模拟，我们将其与现有无法纳入熵约束的方法所得界限进行比较，结果表明在弱混杂设定下，所提界限更为紧致。