用扩散模型的去噪目标提升因果发现的稳定性和效率。
Smoothing the Landscape: Causal Structure Learning via Diffusion Denoising Objectives
- 利用扩散模型的去噪得分匹配平滑梯度，加速收敛。
- 提出自适应k跳环约束，避免矩阵求逆，显著提升运行速度。
- 适用于高维数据和样本-特征不平衡场景，适合实际因果推断任务。
在观测数据中理解因果关系对决策至关重要，通常建模为贝叶斯网络（BNs）或有向无环图（DAGs）。现有方法如NOTEARS和DAG-GNN在高维数据下常面临可扩展性与稳定性问题，尤其在特征-样本不平衡时。本文表明，扩散模型的去噪得分匹配目标可平滑梯度，实现更快、更稳定的收敛。我们提出一种自适应k跳环约束，相比需矩阵求逆的方案显著提升运行效率。该框架命名为去噪扩散因果发现（DDCD）。与生成式扩散模型不同，DDCD利用反向去噪过程推断参数化因果结构而非生成数据。我们在合成基准数据上展示了其竞争性表现，并通过两个真实案例的定性分析验证了方法的实际价值。代码已开源：https://github.com/haozhu233/ddcd。
原文摘要 · Abstract (English)
Understanding causal dependencies in observational data is critical for informing decision-making. These relationships are often modeled as Bayesian Networks (BNs) and Directed Acyclic Graphs (DAGs). Existing methods, such as NOTEARS and DAG-GNN, often face issues with scalability and stability in high-dimensional data, especially when there is a feature-sample imbalance. Here, we show that the denoising score matching objective of diffusion models could smooth the gradients for faster, more stable convergence. We also propose an adaptive k-hop acyclicity constraint that improves runtime over existing solutions that require matrix inversion. We name this framework Denoising Diffusion Causal Discovery (DDCD). Unlike generative diffusion models, DDCD utilizes the reverse denoising process to infer a parameterized causal structure rather than to generate data. We demonstrate the competitive performance of DDCDs on synthetic benchmarking data. We also show that our methods are practically useful by conducting qualitative analyses on two real-world examples. Code is available at this url: https://github.com/haozhu233/ddcd.
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