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.

本文分析了“弱混淆”的因果估计结果，提出了一种有效的线性规划方法来确定因果效应的上下界，并展示了与现有方法相比更紧密的界限，这些方法不能纳入熵限制。

弱交互作用条件下的近似因果效应识别