🤖 AI Summary
This work addresses the challenge in causal discovery where external priors are often heterogeneous and of uncertain reliability—traditional approaches either blindly trust such priors, amplifying errors, or discard them entirely, forfeiting useful signals. To overcome this, we propose PRCD-MAP, which introduces, for the first time, an edge-level trust mechanism that assigns each prior edge an independent learnable weight. This enables fine-grained, adaptive integration of imperfect priors by dynamically modulating the ℓ₁/ℓ₂ mixed regularizer within the maximum a posteriori (MAP) objective. Combining empirical Bayes calibration, Laplace-approximated marginal likelihood, and MLP-based trust propagation, our method achieves substantial performance gains under theoretical safety guarantees: on the CausalTime real-world datasets, it yields significant AUROC improvements (AQI +0.123, Medical +0.043), outperforming PCMCI+ and BayesDAG, while remaining robust in high-dimensional (d=300) and latent-confounded settings.
📝 Abstract
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 \emph{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 \textbf{PRCD-MAP}, a soft prior-consumption layer that assigns \emph{per-edge} trust to an imperfect prior and uses it to modulate a prior-aware $\ell_1$ penalty 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 that 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 $\varepsilon = O(d^2/T)$ -- inheriting the oracle convergence rate. 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 priors when present ($+0.123$ AUROC on AQI, $+0.043$ on Medical over PCMCI+), auto-attenuates on the anonymous-variable Traffic stress test, and retains a lead at $d{=}300$; against BayesDAG~\citep{annadani2023bayesdag} -- 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.