New insights on recovering hidden factors despite noisy data errors
Towards Identifiable Representations under Misspecified Structure
Machine Learning
Summary
Data often comes with hidden influences that are hard to untangle, especially when the noise depends on those hidden factors themselves. The authors study situations where common assumptions about data don't hold, making it harder to identify the hidden causes. They show under what conditions partly accurate recovery is still possible, and develop a learning method to find these hidden factors without supervision. Their tests show this approach works well even when the usual assumptions fail.
What this means in practice
- •For data scientists: Improve extraction of hidden factors from complex data without strong simplifying assumptions about noise.
- •For signal processing engineers: Recover underlying signals when sensor noise depends on those signals and standard noise independence does not hold.
Authors
Yuke Li, Yujia Zheng, Ziyi Chen, Kun Zhang, Heng Huang
Abstract
The presence of noise that depends on the latent variables poses a fundamental challenge to identifiability. Existing results rely on conditional independence among the observations given the latent variables. We study a more general \emph{misspecified structure}, where this conditional factorization does not hold, and establish both precise and approximate identifiability guarantees. We characterize structural misspecification as a perturbed factor analysis problem. For precise identifiability, we establish subspace identifiability under spectral separation and controlled perturbation, followed by component-wise identifiability under structural sparsity. When the precise condition is not guaranteed, we derive an approximate subspace-identifiability theorem. Based on these results, we develop an unsupervised variational estimator for recovering latent variables. Experiments demonstrate the effectiveness of the proposed framework.