让因果发现自动判断外部先验的可信度，避免盲目信任或拒绝。
PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discovery
- 为每个因果边动态分配可信度，通过数据反馈调整信任值。
- 在真实数据上提升0.067~0.123的AUROC，优于传统方法。
- 适合处理不靠谱先验的场景，如大模型生成的因果假设。
不可靠的外部先验在因果发现中带来脆弱权衡：盲目信任会放大错误，完全排斥则浪费信号。真实先验的可靠性差异显著——物理定律可信，大模型建议的边则存疑。现有方法要么忽略先验，要么以统一信任强度强制施加。本文提出PRCD-MAP，引入软先验消费层，为每个边分配独立可信度，并将其融入基于最大后验（MAP）目标的ℓ₁与先验加权ℓ₂正则项。可信度通过拉普拉斯近似边缘似然的贝叶斯经验法校准，并通过MLP在先验图中传播，数据验证的邻域提升可信度，矛盾则抑制。该方法具备群体级安全保证：在先验生成分布上期望下ε-安全，其中ε≤C·acc(1−acc)·d²/T，以参数量级T⁻¹衰减，在先验质量两端趋于零。当先验无信息时，学习到的可信度自动降至下限，方法退化为无先验基线。实验表明，在真实因果时间数据（CausalTime）上，PRCD-MAP有效利用大模型先验（对空气质量/医疗数据，相比无先验基线提升+0.067/+0.089 AUROC；结合基线+先验优势达+0.123/+0.043），在匿名变量交通压力测试中自动降权，且在维度d=300时仍保持优势。相较最接近的软贝叶斯基线BayesDAG，PRCD-MAP在所有CausalTime数据集上匹配仅使用W₀协议下均胜出。四路消融实验显示，经验贝叶斯校准与MLP传播共同贡献主要增益，且每项均为正向。非线性（NAM）与横截面设置扩展表明，校准可信度原则具有设置无关性。
原文摘要 · Abstract (English)
External priors of unknown reliability create a brittle trade-off in causal discovery: blind trust amplifies errors, blind rejection wastes signal. Real priors are also heterogeneously reliable -- physical laws are trustworthy, LLM-suggested edges are speculative -- yet existing methods either ignore priors or impose them through globally uniform trust. We propose PRCD-MAP, a soft prior-consumption layer that assigns per-edge trust to an imperfect prior and uses it to modulate a prior-aware $\ell_1$ and prior-weighted $\ell_2$ regularizer in a MAP objective. Trust is calibrated by empirical Bayes on a Laplace-approximated marginal likelihood and propagated along the prior graph by an MLP, so data-confirmed neighborhoods boost trust and contradictions suppress it. PRCD-MAP enjoys a population-level safety guarantee: it is $\varepsilon$-safe in expectation over the prior-generation distribution, with $\varepsilon\leq C\cdot\mathrm{acc}(1{-}\mathrm{acc})\cdot d^2/T$ at the parametric $T^{-1}$ rate and vanishing at the prior-quality endpoints. When the prior is uninformative, learned trust provably collapses to its floor and the method recovers a no-prior baseline. Empirically, on real CausalTime data PRCD-MAP exploits informative LLM priors (LLM-prior gain $+0.067/+0.089$ AUROC on AQI/Medical over a no-prior PRCD-MAP backbone; combined backbone+prior lead $+0.123/+0.043$ over PCMCI+), auto-attenuates on the anonymous-variable Traffic stress test, and retains a lead at $d{=}300$; against BayesDAG, the closest soft-Bayesian baseline, PRCD-MAP wins on every CausalTime dataset under a matched $W_0$-only protocol. A four-way ablation isolates each component: EB calibration and MLP trust propagation jointly carry the plurality of the gain, with positive sign on every dataset. Extensions to nonlinear (NAM) and cross-sectional settings show the calibrated-trust principle is setting-agnostic.
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