Identifying the effects of causes and causes of effects is vital in virtually
every scientific field. Often, however, the needed probabilities may not be
fully identifiable from the data sources available. This paper shows how
partial identifiability is still possible for several probabilities of
causation. We term this epsilon-identifiability and demonstrate its usefulness
in cases where the behavior of certain subpopulations can be restricted to
within some narrow bounds. In particular, we show how unidentifiable causal
effects and counterfactual probabilities can be narrowly bounded when such
allowances are made. Often those allowances are easily measured and reasonably
assumed. Finally, epsilon-identifiability is applied to the unit selection
problem.

论文展示了如何在某些狭窄的限制边界内实现一些因果关系概率的部分可识别性，其中包括不可识别的因果效应和反事实概率，最后还将此应用到单位选择问题。

因果数量的 Epsilon 可识别性

Epsilon-Identifiability of Causal Quantities

We address the problem of integrating data from multiple, possibly biased,
observational and interventional studies, to eventually compute counterfactuals
in structural causal models. We start from the case of a single observational
dataset affected by a selection bias. We show that the likelihood of the
available data has no local maxima. This enables us to use the causal
expectation-maximisation scheme to compute approximate bounds for partially
identifiable counterfactual queries, which are the focus of this paper. We then
show how the same approach can solve the general case of multiple datasets, no
matter whether interventional or observational, biased or unbiased, by
remapping it into the former one via graphical transformations. Systematic
numerical experiments and a case study on palliative care show the
effectiveness and accuracy of our approach, while hinting at the benefits of
integrating heterogeneous data to get informative bounds in case of partial
identifiability.

本文介绍一种方法，通过数据整合和建立结构性因果模型，在不同条件下解决由选择偏差引起的局部统计问题，并针对数据集的部分可识别性问题提出了一种逼近计算方法。通过系统的实验验证和实例研究，证明了这种方法的可行性和准确性，并揭示了数据整合对于信息界的提高具有积极的作用。