Provable Subspace Identification of Nonlinear Multi-view CCA

Zhiwei Han, Stefan Matthes, Hao Shen
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1947-1982, 2026.

Abstract

We investigate the identifiability of nonlinear canonical correlation analysis ({CCA}) in a multi-view setup, in which each view is generated by applying an unknown nonlinear map to a linear mixture of shared latent variables plus view-private noise. Rather than pursuing exact unmixing, which is known to be ill-posed under general nonlinear mixing, we instead reframe multi-view {CCA} as a basis-invariant subspace identification problem. Under suitable latent priors and spectral separation conditions, we prove that the pairwise population {CCA} objective recovers correlated signal subspaces up to view-wise orthogonal ambiguity. For $N \geq 3$ views, their multi-view aggregation provably isolates the jointly correlated subspaces shared across all views while eliminating view-private variation. We further establish finite-sample statistical consistency guarantees by translating the concentration of empirical cross-covariances into explicit subspace error bounds via spectral perturbation theory. Experiments on synthetic and rendered image datasets support our theoretical findings and illustrate the necessity of the assumed conditions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-han26a, title = {Provable Subspace Identification of Nonlinear Multi-view {CCA}}, author = {Han, Zhiwei and Matthes, Stefan and Shen, Hao}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1947--1982}, 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/han26a/han26a.pdf}, url = {https://proceedings.mlr.press/v337/han26a.html}, abstract = {We investigate the identifiability of nonlinear canonical correlation analysis ({CCA}) in a multi-view setup, in which each view is generated by applying an unknown nonlinear map to a linear mixture of shared latent variables plus view-private noise. Rather than pursuing exact unmixing, which is known to be ill-posed under general nonlinear mixing, we instead reframe multi-view {CCA} as a basis-invariant subspace identification problem. Under suitable latent priors and spectral separation conditions, we prove that the pairwise population {CCA} objective recovers correlated signal subspaces up to view-wise orthogonal ambiguity. For $N \geq 3$ views, their multi-view aggregation provably isolates the jointly correlated subspaces shared across all views while eliminating view-private variation. We further establish finite-sample statistical consistency guarantees by translating the concentration of empirical cross-covariances into explicit subspace error bounds via spectral perturbation theory. Experiments on synthetic and rendered image datasets support our theoretical findings and illustrate the necessity of the assumed conditions.} }
Endnote
%0 Conference Paper %T Provable Subspace Identification of Nonlinear Multi-view CCA %A Zhiwei Han %A Stefan Matthes %A Hao Shen %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-han26a %I PMLR %P 1947--1982 %U https://proceedings.mlr.press/v337/han26a.html %V 337 %X We investigate the identifiability of nonlinear canonical correlation analysis ({CCA}) in a multi-view setup, in which each view is generated by applying an unknown nonlinear map to a linear mixture of shared latent variables plus view-private noise. Rather than pursuing exact unmixing, which is known to be ill-posed under general nonlinear mixing, we instead reframe multi-view {CCA} as a basis-invariant subspace identification problem. Under suitable latent priors and spectral separation conditions, we prove that the pairwise population {CCA} objective recovers correlated signal subspaces up to view-wise orthogonal ambiguity. For $N \geq 3$ views, their multi-view aggregation provably isolates the jointly correlated subspaces shared across all views while eliminating view-private variation. We further establish finite-sample statistical consistency guarantees by translating the concentration of empirical cross-covariances into explicit subspace error bounds via spectral perturbation theory. Experiments on synthetic and rendered image datasets support our theoretical findings and illustrate the necessity of the assumed conditions.
APA
Han, Z., Matthes, S. & Shen, H.. (2026). Provable Subspace Identification of Nonlinear Multi-view CCA. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1947-1982 Available from https://proceedings.mlr.press/v337/han26a.html.

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