OCDaf: Ordered Causal Discovery with Autoregressive Flows
Hamidreza Kamkari∗ Vahid Zehtab∗ Vahid Balazadeh∗ Rahul G. Krishnan University of Toronto, Vector Institute {hamidk, zehtab, vahid,
Abstract
We propose OCDaf, a novel order-based method for learning causal graphs from observational data. We establish the identifiability of causal graphs within multivariate heteroscedastic noise models, a generalization of additive noise models that allow for non-constant noise variances. Drawing upon the structural similarities between these models and affine autoregressive normalizing flows, we introduce a continuous search algorithm to find causal structures. Our experiments demonstrate state-of-the-art performance across the Sachs and SynTReN benchmarks in Structural Hamming Distance (SHD) and Structural Intervention Distance (SID). Furthermore, we validate our identifiability theory across various parametric and nonparametric synthetic datasets and showcase superior performance compared to existing baselines.
中文速览
因果关系推断一直面临两大难题：仅凭观测数据无法区分不同因果结构（可识别性问题），以及有向无环图（DAG）的搜索空间随变量数呈超指数级增长。OCDaf 提出用"位置-尺度噪声模型"（Location-Scale Noise Model，LSNM）来建模数据生成过程——这类模型允许噪声方差随父变量取值变化，比传统加性噪声模型更灵活——并在理论上首次证明了该模型在多变量场景下的因果可识别性。算法层面，作者发现 LSNM 与仿射自回归归一化流（Autoregressive Normalizing Flow）在结构上高度相似，由此设计了一套基于拓扑排序的端到端可微搜索方法，利用 Gumbel-Sinkhorn 和 Gumbel-Top-k 技术在连续空间中优化变量因果顺序，再通过剪枝还原完整因果图。在 Sachs 和 SynTReN 两个标准基准上，OCDaf 在结构汉明距离（SHD）和结构干预距离（SID）两项指标上均达到当前最优水平，同时在多组合成数据集上验证了理论的正确性，表明将异方差噪声纳入因果发现框架能显著提升实际推断能力。
原文 arXiv:2308.07480;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2308.07480v2