AI 中文总结
本文探讨因果模型的马尔可夫等价类不可识别问题，借助特定参数化与几何公式构建因果模型置信集，分析不同情形下模型的包含概率及可实现的极限。
AI 中文摘要
在缺乏强假设的情况下，同一马尔可夫等价类中的因果模型在任何样本量下统计上都无法区分。对于中等样本量，还有可能存在多个此类等价类与数据兼容，这表明应将因果模型的置信集作为证据的恰当呈现方式。来自同一马尔可夫等价类的高斯因果模型的不可识别性，对应于Cox和Wermuth（1993）无约束参数化下的多个逆协方差表示。该参数化避免了会使分布近似复杂化的锥约束，有助于基于标准似然理论构建因果模型的置信集并进行理论分析。借助Evans（2020）的几何公式，我们探究了当生成模型的真实参数值处于可检测性边界时，哪些因果模型最有可能被纳入置信集，划分出包含概率在名义水平上稳定、随样本量缓慢衰减以及随样本量快速衰减的模型。我们还研究了存在两个或更多因果模型同时起作用的情形，探讨混合权重以及混合模型相对于候选模型的几何结构如何与包含概率相互作用。本文的目的是从真实因果机制的结构性质视角，探究因果推理场景中可实现的极限。
英文摘要
Causal models in the same Markov equivalence class are, in the absence of strong assumptions, statistically indistinguishable at any sample size. For modest sample sizes there is also the possibility that several such classes are compatible with the data, pointing to a confidence set of causal models as the appropriate presentation of evidence. Non-identifiability of Gaussian causal models from the same Markov equivalence class corresponds to a plurality of inverse-covariance representations in the unconstrained parametrisation of Cox and Wermuth (1993). This parametrisation, avoiding conic constraints that would otherwise complicate distributional approximations, facilitates construction of, and theoretical analysis for, a confidence set of causal models based on standard likelihood theory. By drawing on a geometric formulation of Evans (2020), we provide insight into which causal models are most likely to be included in the confidence set when the true parameter values of the generating model are at the borderline of detectability, delineating those models whose inclusion probabilities are stable at the nominal level, slowly decaying with sample size, and quickly decaying with sample size. We also study settings in which two or more causal models are in operation, exploring how the mixture weights, and the geometry of the models in the mixture relative to candidate models, interact with the inclusion probabilities. The purpose of the paper is to probe, from the perspective of structural properties of the true causal mechanism, the limits of what is achievable in causal inferential settings.
