Probabilistic Edge Modulation for High-Dimensional Causal Discovery

摘要

Causal discovery in high-dimensional linear Bayesian networks is challenging, even with partial structural knowledge. Such information is often edge-specific and noisy, and naively enforcing uniform shrinkage or hard constraints can induce incorrect or unstable edge selection. We propose Probabilistic Edge Modulation (PEM), a principled probabilistic framework that replaces hard structural constraints with soft, edge-specific modulation via a spike-and-slab formulation. PEM integrates heterogeneous priors into ordering recovery and parent selection through a unified MAP formulation that remains computationally tractable in polynomial time. We establish high-dimensional consistency under both sub-Gaussian and heavy-tailed errors with bounded moments, and demonstrate robustness to prior misspecification. Experiments on synthetic and real retail data demonstrate improved structural stability and graph recovery in sparse and data-limited regimes; in a real e-commerce dataset, probabilistic transfer from a data-rich group stabilizes smaller groups and yields nontrivial graphs that do not collapse to near-empty graphs.