Learning Causal Response Representations through Direct Effect Analysis

Homer Durand, Gherardo Varando, Gustau Camps-Valls

Keywords: Causal Representation Learning, Multivariate Analysis, Conditional Independence Testing, High-Dimensional Causal Inference

TL;DR: We propose a method for disentangling causal response representations by analyzing treatment effects on outcomes, using an algorithm that maximizes evidence against conditional independence.

Abstract: 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.

Code Link: https://github.com/homerdurand/DEA_2025

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission365/Authors, auai.org/UAI/2025/Conference/Submission365/Reproducibility_Reviewers

Submission Number: 365