PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discovery
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PRCD-MAP：在因果发现中学习对不完美先验的信任程度
- 研究问题
- 外部因果图先验可靠性未知且各条边差异较大时，如何利用其信息，同时控制错误先验对因果发现的损害？
- 方法与思路
- 作者在最大后验目标中设置逐边信任加权的正则项，利用经验贝叶斯校准信任，再通过多层感知机沿先验图传播。
- 材料陈述的贡献
- 摘要声称建立对先验生成分布取期望的安全保证，无信息先验时恢复无先验基线，并在多组实验中报告性能收益。
- 阅读关注点
- 应核对安全性的损失定义与期望范围、先验生成假设、拉普拉斯近似误差，以及实验协议、消融和基线调参是否可比。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；平均安全保证不等于每个先验都安全，摘要未列出完整定理条件。
原文摘要
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.