Learning Causal Response Representations through Direct Effect Analysis
This work addresses the problem of uncovering direct causal effects in complex, multivariate settings for researchers in causal inference, though it appears incremental as it bridges existing methods.
The paper tackles the problem of learning causal response representations to identify directions in which a multidimensional outcome is most directly caused by a treatment variable, and it demonstrates empirical effectiveness in simulation and real-world experiments.
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.