在未知因果图下,从混合干预数据中分离出真实因果效应。
Learning Mixtures of Unknown Causal Interventions
- 通过分析干预数据的分布特性,实现对混合数据的成分分离。
- 干预影响越强,所需样本量越少,可高效恢复因果结构。
- 适用于基因组学、经济学等存在干扰性干预数据的领域。
干预能力在学习变量间因果关系中至关重要,广泛应用于基因组学、经济学和机器学习等领域。然而,在许多实际场景中,干预数据生成过程存在噪声:采集的数据并非来自目标干预分布,而是目标与非目标干预分布的混合。本文研究线性结构方程模型(SEMs)中带有高斯加性噪声的混合观测与干预数据的分离问题,且无需已知真实因果图。我们证明,无论采取do干预还是软干预,其产生的分布具有足够多样性与可识别特性,能有效还原混合数据中的各成分。此外,我们发现分离混合数据所需的样本复杂度与干预对变量值方程的影响程度成反比。因此,可在不依赖因果图的前提下,将因果图识别至干预马尔可夫等价类,与无噪声干预数据情形一致。实验模拟验证了该方法在混合数据上进行因果发现的有效性。
原文摘要 · Abstract (English)
The ability to conduct interventions plays a pivotal role in learning causal relationships among variables, thus facilitating applications across diverse scientific disciplines such as genomics, economics, and machine learning. However, in many instances within these applications, the process of generating interventional data is subject to noise: rather than data being sampled directly from the intended interventional distribution, interventions often yield data sampled from a blend of both intended and unintended interventional distributions. We consider the fundamental challenge of disentangling mixed interventional and observational data within linear Structural Equation Models (SEMs) with Gaussian additive noise without the knowledge of the true causal graph. We demonstrate that conducting interventions, whether do or soft, yields distributions with sufficient diversity and properties conducive to efficiently recovering each component within the mixture. Furthermore, we establish that the sample complexity required to disentangle mixed data inversely correlates with the extent of change induced by an intervention in the equations governing the affected variable values. As a result, the causal graph can be identified up to its interventional Markov Equivalence Class, similar to scenarios where no noise influences the generation of interventional data. We further support our theoretical findings by conducting simulations wherein we perform causal discovery from such mixed data.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。