Learning Causal Response Representations through Direct Effect Analysis

2025-03-06

AI Summary

This paper addresses the challenge of identifying the direction of the direct causal effect of a treatment variable on multivariate outcome variables. We propose a low-dimensional response representation method that integrates conditional independence testing with representation learning. Our key contribution is the first formulation of maximizing evidence for conditional independence as a generalized eigenvalue problem, yielding an analytically tractable F-distribution theoretical bound for statistically valid causal inference. We further establish the optimality of the learned representation under both signal-to-noise ratio and Fisher information criteria. The method operates within a generalized eigenvalue decomposition framework, accommodating flexible regression models and enabling task-adaptive modeling. Extensive experiments on synthetic and real-world datasets demonstrate substantial improvements in accuracy for direct causal effect identification, particularly under high dimensionality, noise corruption, and complex confounding—highlighting its effectiveness and robustness.

Technology Category

• Machine Learning: Causal Learning
• Computer Vision: Representation Learning for Vision
• Reasoning under Uncertainty: Causality

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Extract directions where treatment directly causes outcome.
• Formulate optimization to test treatment-outcome conditional independence.
• Provide theoretical guarantees for optimal causal representation learning.

Innovation

• Bridges conditional independence testing with causal learning
• Uses generalized eigenvalue decomposition for optimization
• Maximizes signal-to-noise ratio and Fisher information