突破传统加性噪声假设，实现含隐变量的非加性因果发现。
Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variables
- 基于位置-尺度噪声模型，构建可识别的有向混合图框架。
- 在异方差数据上，算法性能显著优于传统加性方法。
- 适用于存在隐变量且效应影响方差的复杂因果场景。
我们研究在存在隐变量且数据生成过程服从位置-尺度噪声模型（LSNM）时的因果发现问题。现有处理隐混杂变量的方法通常假设噪声为加性，但现实中原因常同时影响结果的均值与方差。本文证明，在满足无弓形条件的有向混合图（ADMG）下，即使存在隐变量，因果结构仍可识别，首次建立了超越加性噪声的因果不足模型的可识别性结果。我们进一步给出在违背无弓形假设时识别因果方向的充分条件。所提出的两阶段算法LSNM-UV具有完全性和正确性，实验表明其在异方差数据上的表现优于加性基线方法。
原文摘要 · Abstract (English)
We study causal discovery from observational data when some variables are hidden and the data-generating process follows a location-scale noise model (LSNM). Existing methods that handle hidden confounders typically assume additive noise, but in practice, causes often modulate not just the mean but also the variance of their effects. We prove that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables, establishing the first identifiability result for causally insufficient models beyond noise additivity. We further provide sufficient conditions for identifying causal direction even when the bow-free assumption is violated. Our two-stage algorithm, LSNM-UV, is sound and complete, and experiments demonstrate improved performance over additive baselines on heteroscedastic data.
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