Towards Identifiable Latent Additive Noise Models
Yuhang Liu, Zhen Zhang, Dong Gong, Erdun Gao, Biwei Huang, Mingming Gong, Anton van den Hengel, Kun Zhang, Javen Qinfeng Shi
TL;DR
This paper introduces a more flexible framework for causal representation learning that relaxes previous assumptions, enabling partial identifiability of latent causal models and demonstrating effectiveness on synthetic, semi-synthetic, and real-world data.
Contribution
It proposes a generalized framework with weaker conditions for identifiability and extends analysis to latent post-nonlinear models, advancing practical causal learning methods.
Findings
Partial identifiability under weaker conditions
Effective learning on synthetic and semi-synthetic datasets
Successful application to human motion analysis
Abstract
Causal representation learning (CRL) offers the promise of uncovering the underlying causal model by which observed data was generated, but the practical applicability of existing methods remains limited by the strong assumptions required for identifiability and by challenges in applying them to real-world settings. Most current approaches are applicable only to relatively restrictive model classes, such as linear or polynomial models, which limits their flexibility and robustness in practice. One promising approach to this problem seeks to address these issues by leveraging changes in causal influences among latent variables. In this vein we propose a more general and relaxed framework than typically applied, formulated by imposing constraints on the function classes applied. Within this framework, we establish partial identifiability results under weaker conditions, including…
Peer Reviews
Decision·Submitted to ICLR 2026
- The document presents thorough intuitions for the modelling choices and assumptions. This makes the whole manuscript clear in terms of readability. - Investigating partial identifiability for a subset of failed assumptions is a very interesting contribution. - The experiments are thorough and the real-world showcase is exciting.
**Comments on theoretical analysis:** - **Clarity:** Please add brief proof sketches after the main theorems: A few indications each explaining the proof idea, how tools from nonlinear ICA/aux-variable methods are used, and explicit pointers to the exact appendix sections/lemmas. - **Sufficiency and necessity:** The paper mentions that their conditions are both **sufficient and necessary**. However, necessity here is considered under their specific model restrictions and assumptions, which is a
- The identifiability results are interesting, building upon the prior works (Liu et al. 2022, 2024), they extend the identifiability of latent causal models with restrictive linear or polynomial assumptions, to more general additive noise causal mechanisms. The extensions for partial identifiability and post non-linear causal models is also significant and novel to the best of my knowledge. - The paper is well-written with a clear description of the various assumptions needed for the theoretic
- One main limitation of the work is that the authors don't mention in Section 3.1 that setup and assumptions 1-3 are very similar to the prior work by Liu et al. 2024 [1]. While the authors state that their novel contribution is only assumption 4 on causal influences, but the way the rest of the setup and assumptions are presented make it seem as if the its a contribution of this work, while the prior work Liu et al. 2024 works with the exact same formulation. It is weird that the authors compa
Node-level or partial identifiability results are newly emerging in CRL literature, and this paper demonstrates that node-level identifiability is achievable up-to-scaling-and-shift under relatively mild conditions on the latent model using perfect/stochastic hard interventions.
The proof of theorem 3.1, while clever, overlooks an assumption. In order to impose the Jacobians of $\mathbf{h}\_{\mathbf{u}^i}$ and $\hat{\mathbf{h}}\_{\mathbf{u}^i}$ to have the same structure, one requires (i) $\mathbf{u}^i$ value to be known, and (ii) $i$ to be known. In interventional CRL language, this is equivalent to requiring access to a perfect intervention (corresponding to using $\mathbf{u}^i$ under assumption (iv)) on node $i$ while knowing a topological order $(1, 2, \dots )$ amon
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Taxonomy
TopicsExplainable Artificial Intelligence (XAI)
MethodsALIGN