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.

翻译：我们提出了一种学习因果响应表示的新方法。该方法旨在提取多维结果中受处理变量最直接影响的维度。通过将条件独立性检验与因果表示学习相结合，我们构建了一个优化问题，该问题在给定条件集的情况下，最大化处理变量与结果之间条件独立性不成立的证据。该公式采用针对特定应用定制的灵活回归模型，从而构建了一个通用框架。该问题通过广义特征值分解进行求解。我们证明，在温和假设下，最大特征值的分布可由已知的$F$分布界定，从而实现可检验的条件独立性。我们还从信噪比和费舍尔信息最大化的角度，为所学表示的最优性提供了理论保证。最后，我们在仿真和真实世界实验中展示了本方法的实证有效性。我们的结果凸显了该框架在揭示复杂多变量场景中直接因果效应方面的实用性。