提出新算法，可精准快速恢复因果图结构，无需人工调参。
Smooth, Sparse, and Stable: Finite-Time Exact Skeleton Recovery via Smoothed Proximal Gradients
- 用光滑近端梯度优化新型无环约束，实现精确图结构恢复。
- 理论证明可在有限步内完全识别真实因果结构，不依赖启发式阈值。
- 适合需要高精度因果推断的研究者，尤其适用于小样本场景。
连续优化显著推动了因果发现的发展，但现有方法（如 NOTEARS）通常仅能保证收敛到平稳点，常产生稠密加权矩阵，需人为后处理阈值才能还原有向无环图（DAG）。这一连续优化与离散图结构间的鸿沟仍是根本性挑战。本文提出混合阶无环约束（AHOC），并通过光滑近端梯度（SPG-AHOC）进行优化。利用近端算法的流形识别性质，我们建立了严格的理论保证：在标准可识别性假设下，SPG-AHOC 可在有限迭代内精确恢复真实 DAG 支撑（结构），即使在优化平滑近似时亦成立。该结果消除了结构模糊性，算法输出的图具有精确零值，无需启发式截断。实验证明，SPG-AHOC 达到当前最优准确率，强有力支持了有限时间识别理论。
原文摘要 · Abstract (English)
Continuous optimization has significantly advanced causal discovery, yet existing methods (e.g., NOTEARS) generally guarantee only asymptotic convergence to a stationary point. This often yields dense weighted matrices that require arbitrary post-hoc thresholding to recover a DAG. This gap between continuous optimization and discrete graph structures remains a fundamental challenge. In this paper, we bridge this gap by proposing the Hybrid-Order Acyclicity Constraint (AHOC) and optimizing it via the Smoothed Proximal Gradient (SPG-AHOC). Leveraging the Manifold Identification Property of proximal algorithms, we provide a rigorous theoretical guarantee: the Finite-Time Oracle Property. We prove that under standard identifiability assumptions, SPG-AHOC recovers the exact DAG support (structure) in finite iterations, even when optimizing a smoothed approximation. This result eliminates structural ambiguity, as our algorithm returns graphs with exact zero entries without heuristic truncation. Empirically, SPG-AHOC achieves state-of-the-art accuracy and strongly corroborates the finite-time identification theory.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。