Provable Affine Identifiability of Nonlinear CCA under Latent Distributional Priors

• URL: http://arxiv.org/abs/2510.04758v1
• Date: Mon, 06 Oct 2025 12:35:07 GMT
• Title: Provable Affine Identifiability of Nonlinear CCA under Latent Distributional Priors
• Abstract summary: We prove affine identifiability for a broad class of latent distributions in the population setting.<n>We show that whitening is essential for ensuring boundedness and well-conditioning.<n>Beyond the population setting, we prove that ridge-regularized empirical CCA converges to its population counterpart.
• Score: 7.550362088105815
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we establish conditions under which nonlinear CCA recovers the ground-truth latent factors up to an orthogonal transform after whitening. Building on the classical result that linear mappings maximize canonical correlations under Gaussian priors, we prove affine identifiability for a broad class of latent distributions in the population setting. Central to our proof is a reparameterization result that transports the analysis from observation space to source space, where identifiability becomes tractable. We further show that whitening is essential for ensuring boundedness and well-conditioning, thereby underpinning identifiability. Beyond the population setting, we prove that ridge-regularized empirical CCA converges to its population counterpart, transferring these guarantees to the finite-sample regime. Experiments on a controlled synthetic dataset and a rendered image dataset validate our theory and demonstrate the necessity of its assumptions through systematic ablations.

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