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arXiv 2603.04780cs.LGstat.ML
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线性非高斯潜在变量循环因果模型中的分布等价性:特征化与学习

Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning

Carnegie Mellon University(卡内基梅隆大学);FernUniversität in Hagen(哈根函授大学);MBZUAI(穆罕默德·本·扎耶德人工智能大学)

Haoyue Dai, Immanuel Albrecht, Peter Spirtes, Kun Zhang

AI总结:

本文提出了一种线性非高斯潜在变量循环因果模型的分布等价性特征化方法,填补了无结构假设的因果发现空白。

摘要:

因果发现中的潜在变量是一个基本任务。然而,大多数现有方法依赖于强结构假设,例如强制对潜在变量进行特定的指示模式或限制它们如何与其他变量相互作用。我们认为,一般化、无结构假设的方法的核心障碍在于缺乏等价性特征化:在不知道什么可以被识别的情况下,通常无法设计出如何识别它的方法。在本工作中,我们旨在为线性非高斯模型填补这一空白。我们建立了两个具有任意潜在结构和循环的图的分布等价图准则,即它们诱导相同的观察分布集。我们方法的关键是一个新的工具,边秩约束,这在更广泛的潜在变量因果发现工具箱中填补了缺失的一块。我们进一步提供了一种遍历整个等价类的程序,并开发了一种从数据中恢复模型的算法,直到这种等价性。据我们所知,这是首次在任何参数设置中没有结构假设的情况下,具有潜在变量的等价性特征化,因此是首次无结构假设的发现方法。代码和交互演示可在https://equiv.cc上获得。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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