arXiv:2509.12981cs.LGstat.ML2025-09被引 1

通过分位数偏效应揭示因果方向,无需假设噪声机制。

Causal Discovery via Quantile Partial Effect

  • 基于分位数回归的偏效应统计量识别因果关系
  • 在多个双变量数据集上验证了因果方向判断有效性
  • 适用于无噪声假设的多变量场景,适合因果推断研究者

分位数偏效应(QPE)是条件分位数回归的统计量,用于衡量协变量在不同分位水平上的影响。理论表明,当因果对结果的QPE位于有限线性张量空间时,因果关系可从观测分布中唯一确定,该结果推广了基于加性异方差噪声等函数因果模型的可识别性结论。由于QPE完全基于观测层面,该参数假设无需考虑机制、噪声或马尔可夫性,仅利用观测分布形状特征的不对称性。通过对估计的QPE进行基函数检验,可区分因果方向,在大量双变量因果发现数据集上表现出良好效果。对于多变量情形,借助QPE与得分函数的紧密联系,我们发现费舍尔信息足以作为统计指标,在对QPE二阶矩做出假设条件下确定因果顺序。在多个合成及真实世界多变量因果发现数据集上验证了该方法可行性。

原文摘要 · Abstract (English)

Quantile Partial Effect (QPE) is a statistic associated with conditional quantile regression, measuring the effect of covariates at different levels. Our theory demonstrates that when the QPE of cause on effect is assumed to lie in a finite linear span, cause and effect are identifiable from their observational distribution. This generalizes previous identifiability results based on Functional Causal Models (FCMs) with additive, heteroscedastic noise, etc. Meanwhile, since QPE resides entirely at the observational level, this parametric assumption does not require considering mechanisms, noise, or even the Markov assumption, but rather directly utilizes the asymmetry of shape characteristics in the observational distribution. By performing basis function tests on the estimated QPE, causal directions can be distinguished, which is empirically shown to be effective in experiments on a large number of bivariate causal discovery datasets. For multivariate causal discovery, leveraging the close connection between QPE and score functions, we find that Fisher Information is sufficient as a statistical measure to determine causal order when assumptions are made about the second moment of QPE. We validate the feasibility of using Fisher Information to identify causal order on multiple synthetic and real-world multivariate causal discovery datasets.

因果发现分位数回归统计推断多变量分析

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