从多维结果中提取治疗变量的直接因果效应方向。
Learning Causal Response Representations through Direct Effect Analysis
- 通过条件独立性检验构建优化目标，聚焦治疗与结果的直接关联
- 最大特征值服从已知F分布，可进行可验证的条件独立性检验
- 理论保证信号噪声比和费雪信息最大化，适合复杂多变量场景
我们提出一种学习因果响应表示的新方法，旨在提取多维结果中受处理变量最直接因果影响的方向。通过将条件独立性检验与因果表示学习结合，我们构建了一个优化问题，以最大化在给定调节集下，处理变量与结果间条件独立性的反证据。该方法采用针对具体应用设计的灵活回归模型，形成通用框架，通过广义特征值分解求解。在弱假设下，我们证明了最大特征值的分布可被已知的F分布所界定，从而实现可检验的条件独立性判断。此外，我们提供了所学表示在信噪比和费雪信息最大化方面的理论最优性保证。最后，在模拟和真实世界实验中展示了该方法的实证有效性。结果表明，该框架在复杂多变量环境中揭示直接因果效应方面具有显著价值。
原文摘要 · Abstract (English)
We propose a novel approach for learning causal response representations. Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable. By bridging conditional independence testing with causal representation learning, we formulate an optimisation problem that maximises the evidence against conditional independence between the treatment and outcome, given a conditioning set. This formulation employs flexible regression models tailored to specific applications, creating a versatile framework. The problem is addressed through a generalised eigenvalue decomposition. We show that, under mild assumptions, the distribution of the largest eigenvalue can be bounded by a known $F$-distribution, enabling testable conditional independence. We also provide theoretical guarantees for the optimality of the learned representation in terms of signal-to-noise ratio and Fisher information maximisation. Finally, we demonstrate the empirical effectiveness of our approach in simulation and real-world experiments. Our results underscore the utility of this framework in uncovering direct causal effects within complex, multivariate settings.
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