mlsanityData to 7 Oct 2026

PRCD-MAP: Learning How Much to Trust Imperfect Priors in Causal Discovery

arXiv 2605.01669 ↗First posted 3 May 2026stat.ML cs.LG stat.MEcited by 0

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Abstract (arXiv)

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 ℓ1 and prior-weighted ℓ2 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≤ C·acc(1-acc)· d2/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 W0-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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 25 of its 53 references that are in the map. First posted on arXiv 3 May 2026.

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References · 25

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  2. 2023Causal Reasoning and Large Language Models: Opening a New Frontier for Causalitycited by 348
  3. 2020Neural Additive Models: Interpretable Machine Learning with Neural Netscited by 318
  4. 2019Gradient-Based Neural DAG Learningcited by 227
  5. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  6. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 198
  7. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
  8. 2013Learning Bayesian Networks: The Combination of Knowledge and Statistical Datacited by 185
  9. 2013Causal Inference and Causal Explanation with Background Knowledgecited by 168
  10. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  11. 2020Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasetscited by 136
  12. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
13 more
  1. 2021DiBS: Differentiable Bayesian Structure Learningcited by 105
  2. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  3. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 46
  4. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  5. 2021The impact of prior knowledge on causal structure learningcited by 35
  6. 2023CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discoverycited by 35
  7. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  8. 2022Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noisecited by 30
  9. 2020Neural Additive Vector Autoregression Models for Causal Discovery in Time Seriescited by 28
  10. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  11. 2024Dagma-DCE: Interpretable, Non-Parametric Differentiable Causal Discoverycited by 6
  12. 2025Differentiable Constraint-Based Causal Discoverycited by 4
  13. 2024Use of Prior Knowledge to Discover Causal Additive Models with Unobserved Variables and its Application to Time Series Datacited by 2

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