On Causal Representation Learning with Internal Auxiliaries

Kwonho Kim, Heejeong Nam, Inwoo Hwang, Sanghack Lee
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:3061-3082, 2026.

Abstract

Causal representation learning typically achieves identifiability using auxiliary variables external to the mixing process. This fails when observable sources act as internal mixing inputs whose entanglement invalidates standard volume-change proofs. We introduce a framework that treats observable sources as internal auxiliaries. We establish identifiability when all observed internal sources are used as conditioning variables. Under a volume-preserving mixing assumption, suitable variability conditions, and additional alignment conditions on the learned model, the unobserved source subspaces are identifiable up to an Independent Subspace Analysis ({ISA})-style equivalence class—a permutation of conditionally independent subspaces with within-subspace invertible transformations. In practice, we approximate the volume-preserving restriction with encoders that stabilize the induced distortion. Leveraging the known causal graph, we further propose a scheme that selects conditioning sources so as to preserve fine-grained factorizations of the unobserved sources. Experiments show improved recovery over representative auxiliary-based baselines in settings where treating internal sources as external conditioners can induce cross-factor leakage.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-kim26e, title = {On Causal Representation Learning with Internal Auxiliaries}, author = {Kim, Kwonho and Nam, Heejeong and Hwang, Inwoo and Lee, Sanghack}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {3061--3082}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/kim26e/kim26e.pdf}, url = {https://proceedings.mlr.press/v337/kim26e.html}, abstract = {Causal representation learning typically achieves identifiability using auxiliary variables external to the mixing process. This fails when observable sources act as internal mixing inputs whose entanglement invalidates standard volume-change proofs. We introduce a framework that treats observable sources as internal auxiliaries. We establish identifiability when all observed internal sources are used as conditioning variables. Under a volume-preserving mixing assumption, suitable variability conditions, and additional alignment conditions on the learned model, the unobserved source subspaces are identifiable up to an Independent Subspace Analysis ({ISA})-style equivalence class—a permutation of conditionally independent subspaces with within-subspace invertible transformations. In practice, we approximate the volume-preserving restriction with encoders that stabilize the induced distortion. Leveraging the known causal graph, we further propose a scheme that selects conditioning sources so as to preserve fine-grained factorizations of the unobserved sources. Experiments show improved recovery over representative auxiliary-based baselines in settings where treating internal sources as external conditioners can induce cross-factor leakage.} }
Endnote
%0 Conference Paper %T On Causal Representation Learning with Internal Auxiliaries %A Kwonho Kim %A Heejeong Nam %A Inwoo Hwang %A Sanghack Lee %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-kim26e %I PMLR %P 3061--3082 %U https://proceedings.mlr.press/v337/kim26e.html %V 337 %X Causal representation learning typically achieves identifiability using auxiliary variables external to the mixing process. This fails when observable sources act as internal mixing inputs whose entanglement invalidates standard volume-change proofs. We introduce a framework that treats observable sources as internal auxiliaries. We establish identifiability when all observed internal sources are used as conditioning variables. Under a volume-preserving mixing assumption, suitable variability conditions, and additional alignment conditions on the learned model, the unobserved source subspaces are identifiable up to an Independent Subspace Analysis ({ISA})-style equivalence class—a permutation of conditionally independent subspaces with within-subspace invertible transformations. In practice, we approximate the volume-preserving restriction with encoders that stabilize the induced distortion. Leveraging the known causal graph, we further propose a scheme that selects conditioning sources so as to preserve fine-grained factorizations of the unobserved sources. Experiments show improved recovery over representative auxiliary-based baselines in settings where treating internal sources as external conditioners can induce cross-factor leakage.
APA
Kim, K., Nam, H., Hwang, I. & Lee, S.. (2026). On Causal Representation Learning with Internal Auxiliaries. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:3061-3082 Available from https://proceedings.mlr.press/v337/kim26e.html.

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