arXiv:2609.03442cs.LG2026-09

研究发现专家先验约束在因果发现中常失效,原因有二:误删真边与方向不可区分。

Guide, Not Bind: Why Defeasible Priors Fail in Augmented Lagrangian Causal Discovery

论文配图:Guide, Not Bind: Why Defeasible Priors Fail in Augmented Lagrangian Causal Discovery
图 1 · 摘自论文原文
  • 提出自适应松弛机制需满足三个条件,现有方法DADU违反全部条件
  • 实验显示错误先验导致真边被压制达87%~97%概率,且方向无法区分
  • 适合关注因果推理鲁棒性、模型可解释性的研究人员阅读

可微因果发现方法常将专家先验作为禁止边约束,通过增广拉格朗日法(ALM)惩罚实现,假设数据会自适应地放松并最终覆盖矛盾规则。本文指出这种‘引导而非绑定’的设计存在两个独立且精确描述的失败原因。首先,顺序惩罚提升的ALM会在反事实检验前就抑制本应存在的真实边;我们给出三个必要条件以避免此问题,证明所研究的自然松弛规则DADU违反全部条件,并在4至32个节点的图上3072次训练中验证:单个错误先验使真边被抑制的比例达87%–97%。其次,标准相关性匹配目标函数将真实边与其反向连接的代价均设为恰好$2r^2$,并非模型不可识别,而是归因于相关性归一化舍弃了方差信息;而协方差匹配则可保证方向间至少$w_0^4$的可分差距。

原文摘要 · Abstract (English)

Differentiable causal discovery methods increasingly encode expert priors as forbidden-edge constraints enforced by an Augmented Lagrangian (ALM) penalty, on the assumption that a data-adaptive relaxation mechanism will discount and eventually override a rule the data consistently contradicts. We show this design, which we call \emph{guide, not bind}, fails for two independent, precisely characterized reasons, and that directly repairing both restores it only partially. First, sequential penalty-ramping ALM suppresses a wrongly-forbidden true edge before any counterfactual check can detect it: we give three necessary conditions any adaptive relaxation must satisfy to avoid this (Proposition~\ref{prop:conditions}), prove that DADU---the natural relaxation rule this paper introduces as the object of study---violates all three (Corollary~\ref{cor:dadu_failure}), and confirm the failure across 3{,}072 training runs spanning graphs from 4 to 32 nodes, where a single wrong prior suppresses a true edge in 87--97\% of trials under DADU. Second, and independent of any fix to the mechanism, we prove in closed form that the standard correlation-matching objective ties a true edge and its reverse to an identical cost of exactly $2r^2$ (Lemma~\ref{lem:tie}), not because the underlying equal-variance model is unidentifiable, but because normalizing to correlation discards exactly the variance information that would make it identifiable; covariance matching instead separates the two directions by a provable margin of at least $w_0^4$ (Lemma~\ref{lem:separation}).

因果发现约束优化可微学习模型可靠性

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