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.

翻译：我们研究当某些变量隐藏且数据生成过程遵循位置-尺度噪声模型（LSNM）时，基于观测数据的因果发现。现有处理隐藏混杂因子的方法通常假设噪声是可加的，但在实践中，原因往往不仅调节结果的均值，还调节其方差。我们证明满足无弓形条件的有向混合图（ADMGs）在含隐变量的LSNM下是可识别的，这建立了因果不足模型在超越噪声可加性方面的首个可识别性结果。我们还为即使在违反无弓形假设的情况下识别因果方向提供了充分条件。我们的两阶段算法LSNM-UV是完备且可靠的，实验表明在异方差数据上其性能优于可加基线方法。