Causal Representation Learning from General Environments under Nonparametric Mixing

2026-04-26

AI Summary

Existing approaches to identifying latent causal variables and their structural relationships from low-level observations—such as pixels—often rely on strong assumptions, including specific interventions or linear mixing, which limit their applicability in real-world settings. This work proposes a novel framework that, under the weak assumption that causal mechanisms exhibit sufficient variation up to their third-order derivatives across generic environments, achieves full identifiability of both nonlinear latent causal graphs and nonparametric mixtures for the first time. By integrating higher-order derivative analysis, nonparametric function identification, and causal representation theory, the method substantially relaxes requirements on environmental variation while attaining identification accuracy comparable to or better than existing approaches under far more general and realistic conditions.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.

Problem

• causal representation learning
• general environments
• nonparametric mixing
• latent causal variables
• directed acyclic graphs

Innovation

• causal representation learning
• nonparametric mixing
• general environments
• latent DAG recovery
• nonlinear causal models