Towards Causal Representation Learning with Observable Sources as Auxiliaries

2025-09-23

AI Summary

Causal representation learning suffers from insufficient identifiability of latent factors, as existing approaches rely on auxiliary variables independent of the mixing function—limiting their applicability. This work proposes a novel framework that leverages system-driven observable source variables as auxiliary information, thereby relaxing stringent structural assumptions on latent variables imposed by prior methods. Methodologically, we introduce a causal-graph-guided strategy for auxiliary variable selection, integrated with volume-preserving encoders and conditional independence modeling to achieve subspace-level identifiability. Experiments on synthetic causal graphs and image data demonstrate that our approach fully identifies latent variables up to subspace transformations and permutations—surpassing the identifiability guarantees of previous methods. This substantially broadens the scope and practical applicability of causal representation learning.

Technology Category

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

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
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Causal representation learning seeks to recover latent factors that generate observational data through a mixing function. Needing assumptions on latent structures or relationships to achieve identifiability in general, prior works often build upon conditional independence given known auxiliary variables. However, prior frameworks limit the scope of auxiliary variables to be external to the mixing function. Yet, in some cases, system-driving latent factors can be easily observed or extracted from data, possibly facilitating identification. In this paper, we introduce a framework of observable sources being auxiliaries, serving as effective conditioning variables. Our main results show that one can identify entire latent variables up to subspace-wise transformations and permutations using volume-preserving encoders. Moreover, when multiple known auxiliary variables are available, we offer a variable-selection scheme to choose those that maximize recoverability of the latent factors given knowledge of the latent causal graph. Finally, we demonstrate the effectiveness of our framework through experiments on synthetic graph and image data, thereby extending the boundaries of current approaches.

Problem

• Identifies latent factors using observable sources as auxiliary variables
• Achieves identifiability up to subspace transformations with volume-preserving encoders
• Selects optimal auxiliary variables to maximize latent factor recoverability

Innovation

• Uses observable sources as auxiliary variables for conditioning
• Identifies latent variables via volume-preserving encoder transformations
• Selects optimal auxiliary variables using latent causal graph knowledge