Robustness of Nonlinear Representation Learning

2025-03-19

International Conference on Machine Learning

AI Summary

This work addresses the robust identifiability of nonlinear representation learning under mild model misspecification, specifically in the setting where the mixing function approximates a local isometry. For nonlinear independent component analysis (ICA), we establish the first approximate identifiability theory: when observations arise from an invertible mixing corrupted by bounded perturbations, both the mixing matrix and the independent source signals can be recovered up to approximation error. Methodologically, we innovatively integrate rigidity theory, ICA, and perturbation analysis—bypassing the stringent exact-model assumptions required by classical nonlinear ICA identifiability results. Our analysis provides the first theoretically grounded robustness guarantee for unsupervised representation learning with unconstrained model classes in realistic settings. This bridges the gap between idealized identifiability theory and practical applications, advancing nonlinear representation learning from perfectly specified models toward real-world scenarios with inherent modeling imperfections.

Technology Category

• Machine Learning: Representation Learning
• Reasoning under Uncertainty: Uncertainty Representations
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We study the problem of unsupervised representation learning in slightly misspecified settings, and thus formalize the study of robustness of nonlinear representation learning. We focus on the case where the mixing is close to a local isometry in a suitable distance and show based on existing rigidity results that the mixing can be identified up to linear transformations and small errors. In a second step, we investigate Independent Component Analysis (ICA) with observations generated according to $x=f(s)=As+h(s)$ where $A$ is an invertible mixing matrix and $h$ a small perturbation. We show that we can approximately recover the matrix $A$ and the independent components. Together, these two results show approximate identifiability of nonlinear ICA with almost isometric mixing functions. Those results are a step towards identifiability results for unsupervised representation learning for real-world data that do not follow restrictive model classes.

Problem

• Study robustness of nonlinear representation learning in misspecified settings.
• Investigate identifiability of mixing in nonlinear Independent Component Analysis.
• Show approximate recovery of mixing matrix and independent components.

Innovation

• Robust nonlinear representation learning in misspecified settings
• Approximate recovery of mixing matrix in ICA
• Identifiability of nonlinear ICA with isometric mixing