区分变量均值与方差的因果关系,揭示异方差数据背后的双重因果结构。
Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data
- 基于贝叶斯框架,分离推断均值与方差的独立因果图。
- 在合成、半合成与真实数据上准确恢复双因果结构,优于现有方法。
- 支持不确定性量化,适合需要可解释干预的科学决策场景。
异方差性——即变量方差随其他变量变化——在真实数据中普遍存在,从统计矩角度理解其成因对科学发现和决策至关重要。然而,传统因果发现仅输出单一无矩图,无法区分哪些因素影响均值、哪些影响方差,限制了可解释性与下游干预设计。本文提出一种贝叶斯、矩驱动的因果发现框架,从异方差观测数据中推断独立的均值与方差因果图。首先建立了充分条件,确保两类图可分离识别;在此基础上,构建变分推理方法,学习两图的后验分布,实现对边、路径及子图等结构特征的合理不确定性量化。为应对异方差模型中双重图结构带来的参数优化挑战,采用曲率感知优化策略,并引入基于节点顺序的先验知识,提升样本效率。在合成、半合成与真实数据上的实验表明,该方法能准确恢复均值与方差结构,显著优于现有最优基线。
原文摘要 · Abstract (English)
Heteroscedasticity -- where the variance of a variable changes with other variables -- is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and decision-making. However, standard causal discovery does not reveal which causes act on the mean versus the variance, as it returns a single moment-agnostic graph, limiting interpretability and downstream intervention design. We propose a Bayesian, moment-driven causal discovery framework that infers separate \textit{mean} and \textit{variance} causal graphs from observational heteroscedastic data. We first derive the identification results by establishing sufficient conditions under which these two graphs are separately identifiable. Building on this theory, we develop a variational inference method that learns a posterior distribution over both graphs, enabling principled uncertainty quantification of structural features (e.g., edges, paths, and subgraphs). To address the challenges of parameter optimization in heteroscedastic models with two graph structures, we take a curvature-aware optimization approach and develop a prior incorporation technique that leverages domain knowledge on node orderings, improving sample efficiency. Experiments on synthetic, semi-synthetic, and real data show that our approach accurately recovers mean and variance structures and outperforms state-of-the-art baselines.
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