Confidence in Causal Inference under Structure Uncertainty in Linear Causal Models with Equal Variances
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等误差方差线性因果模型中结构不确定性下的置信推断
- 研究问题
- 在线性且误差方差相等的因果模型中，如何为总因果效应构造置信区域，同时计入图结构学习和效应参数估计的不确定性？
- 方法与思路
- 作者针对观察数据可识别的等误差方差线性模型，提出检验反演框架，将候选结构与效应大小的不确定性纳入推断。
- 材料陈述的贡献
- 摘要称，该框架能够同时反映因果结构和非零效应数值的不确定性，回应先学习图再视其已知所造成的过度乐观区间。
- 阅读关注点
- 应核对等误差方差及图模型条件、检验反演的覆盖率保证、候选图搜索方法，以及结构不确定性导致的区域形状。
- 阅读边界
- 所给来源为 arXiv 预印本，同行评审未经核实；摘要未提供检验细节、计算负担或假设偏离时的覆盖表现。
原文摘要
Inferring the effect of interventions within complex systems is a fundamental problem of statistics. A widely studied approach employs structural causal models that postulate noisy functional relations among a set of interacting variables. The underlying causal structure is then naturally represented by a directed graph whose edges indicate direct causal dependencies. In a recent line of work, additional assumptions on the causal models have been shown to render this causal graph identifiable from observational data alone. One example is the assumption of linear causal relations with equal error variances that we will take up in this work. When the graph structure is known, classical methods may be used for calculating estimates and confidence intervals for causal effects. However, in many applications, expert knowledge that provides an a priori valid causal structure is not available. Lacking alternatives, a commonly used two-step approach first learns a graph and then treats the graph as known in inference. This, however, yields confidence intervals that are overly optimistic and fail to account for the data-driven model choice. We argue that to draw reliable conclusions, it is necessary to incorporate the remaining uncertainty about the underlying causal structure in confidence statements about causal effects. To address this issue, we present a framework based on test inversion that allows us to give confidence regions for total causal effects that capture both sources of uncertainty: causal structure and numerical size of nonzero effects.