首次实现无结构假设的潜变量因果模型等价性刻画，推动因果发现新范式。
Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning
- 提出边秩约束新工具，解决潜变量循环模型等价性判定难题
- 建立任意潜变量与环路结构下的分布等价图判据
- 首个无需强假设的因果发现算法，适合复杂真实数据场景
潜变量因果发现是基础任务，但现有方法多依赖强结构假设，如强制潜变量指标模式或限制其交互方式。我们指出，缺乏等价性刻画是实现通用、无假设方法的核心障碍：若不知何者可识别，便无法设计识别方法。本文针对线性非高斯潜变量循环模型，首次建立两个图在任意潜变量结构和环路下分布等价（即诱导相同观测分布集）的图判据。核心在于提出边秩约束这一新工具，填补了更广泛设定下潜变量因果发现的工具空白。进一步提供遍历整个等价类的程序，并开发从数据恢复模型至等价类的算法。据我们所知，这是首个在参数化设定下无结构性假设的等价性刻画，也是首个真正无假设的因果发现方法。代码与交互演示见 https://equiv.cc。
原文摘要 · Abstract (English)
Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalence class and develop an algorithm to recover models from data up to such equivalence. To our knowledge, this is the first equivalence characterization with latent variables in any parametric setting without structural assumptions, and hence the first structural-assumption-free discovery method. Code and an interactive demo are available at https://equiv.cc.
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