Directional Evidence Guided Search-Space Reduction for Exact DAG Learning

2026-10-06

AI Summary

This study addresses the prohibitive computational burden of combinatorial search in exact DAG learning, which arises from the exponential growth of candidate parent sets. To overcome this challenge, we propose DECO, a nonparametric mixture framework that pioneers directional evidence extraction to construct admissible parent sets, thereby substantially reducing the search space while preserving all plausible edge orientations without requiring prespecified parametric models. Theoretically, we prove that DECO achieves an exponential reduction in the search space. Extensive experiments on benchmark Bayesian networks and synthetic datasets demonstrate that the proposed method significantly lowers computational complexity while maintaining highly competitive performance in structure recovery accuracy and Structural Hamming Distance (SHD).

Abstract

Learning a directed acyclic graph (DAG) from observational data is a challenging combinatorial problem due to the exponential growth in the number of candidate parent-set configurations. Existing exact score-based methods often require computationally intensive combinatorial search, whereas constraint-based methods can become unreliable or computationally demanding as graph size and conditioning-set complexity increase. We develop a non-parametric hybrid framework, referred to as DECO (Directional Evidence-guided Configuration Optimization), that extracts dependency and directional evidence from observation data to construct admissible parent sets prior to exact optimization. It reduces the optimization search space by eliminating empirically unsupported parent configurations while preserving flexibility for all plausible edge orientations. Theoretical analysis establishes an exponential reduction in the admissible parent-set configuration space and quantifies how bounded edge-level omission affects the probability of retaining the true parent structure. Experiments on benchmark Bayesian networks and synthetic discrete and continuous DAGs demonstrate substantial search-space reduction while achieving competitive structure-recovery performance, with favorable structural Hamming distance across many evaluated settings. These results show that directional evidence can provide an effective preprocessing mechanism for reducing the computational burden of exact DAG learning without requiring a fixed parametric structural~model.

Problem

• Directed Acyclic Graph Learning
• Combinatorial Optimization
• Search Space Reduction
• Structure Recovery

Innovation

• DAG learning
• search-space reduction
• directional evidence
• non-parametric hybrid framework
• exact optimization