Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning
arXiv:2603.04780v1 Announce Type: new Abstract: Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalenc
arXiv:2603.04780v1 Announce Type: new Abstract: Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalence class and develop an algorithm to recover models from data up to such equivalence. To our knowledge, this is the first equivalence characterization with latent variables in any parametric setting without structural assumptions, and hence the first structural-assumption-free discovery method. Code and an interactive demo are available at https://equiv.cc.
Executive Summary
This article presents a novel approach to causal discovery with latent variables in linear non-Gaussian models, overcoming the limitations of existing methods that rely on strong structural assumptions. The authors establish a graphical criterion for distributional equivalence, enabling the identification of models with arbitrary latent structure and cycles. They introduce edge rank constraints, a new tool for latent-variable causal discovery, and provide a procedure to traverse the equivalence class and an algorithm to recover models from data. This work is significant as it offers the first equivalence characterization with latent variables in a parametric setting without structural assumptions.
Key Points
- ▸ Distributional equivalence characterization for linear non-Gaussian models with latent variables
- ▸ Introduction of edge rank constraints for latent-variable causal discovery
- ▸ Development of a procedure to traverse the equivalence class and an algorithm for model recovery
Merits
Methodological Innovation
The article introduces a novel approach to causal discovery, overcoming existing limitations and providing a more general and flexible framework.
Demerits
Computational Complexity
The new approach may require significant computational resources, potentially limiting its applicability to large-scale datasets.
Expert Commentary
This article represents a significant advancement in the field of causal discovery, providing a more general and flexible framework for understanding complex systems with latent variables. The introduction of edge rank constraints and the development of a procedure to traverse the equivalence class are particularly noteworthy contributions. However, the computational complexity of the new approach may require further optimization to ensure its applicability to large-scale datasets. Overall, this work has the potential to inform a wide range of fields and policy decisions, and its implications should be carefully considered by researchers and practitioners.
Recommendations
- ✓ Further research is needed to optimize the computational efficiency of the new approach and to explore its applications in various fields.
- ✓ The development of user-friendly software and interactive demos, such as the one provided by the authors, can facilitate the adoption of the new method by researchers and practitioners.