Learning Causal Response Representations through Direct Effect Analysis

• URL: http://arxiv.org/abs/2503.04358v1
• Date: Thu, 06 Mar 2025 12:01:41 GMT
• Title: Learning Causal Response Representations through Direct Effect Analysis
• Authors: Homer Durand, Gherardo Varando, Gustau Camps-Valls,
• Abstract summary: We propose a novel approach for learning causal response representations.<n>Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable.
• Score: 3.881388090216841
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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