On inferential equivalence classes of causal models
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因果模型的推断等价类
- 研究问题
- 当不同因果模型在统计上无法区分，且有限样本同时支持多个等价类时，如何呈现因果证据并刻画可辨识性的边界？
- 方法与思路
- 作者利用高斯因果模型的无约束逆协方差参数化，以似然理论构造模型置信集，并借助几何表述分析边界参数及混合机制。
- 材料陈述的贡献
- 摘要称，该框架区分模型纳入概率保持名义水平、缓慢衰减与快速衰减的情形，并分析混合权重和模型几何的共同影响。
- 阅读关注点
- 应核对置信集的构造与覆盖对象、可检测性边界的定义，以及不同衰减结论和混合机制分析分别依赖哪些条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未获核实；摘要未列出完整正则条件，也不足以判断置信集的实际计算表现。
原文摘要
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.