Generalization Guarantees for Representation Learning via Data-Dependent Gaussian Mixture Priors

2025-02-21

AI Summary

This paper addresses the insufficient theoretical guarantees on generalization error in representation learning by proposing a data-dependent Gaussian mixture prior modeling framework. Methodologically, it integrates the Minimum Description Length (MDL) principle with variational inference, constructing a symmetric prior based on training- and test-time latent variables and deriving tight expected and tail bounds on generalization error via the relative entropy. Theoretically, it reveals two key insights: (i) the prior learning process naturally induces a weighted attention mechanism, and (ii) the generalization bound explicitly incorporates encoder architectural simplicity. Empirically, the approach significantly outperforms VIB and CDVIB across multiple benchmarks, yielding tighter theoretical bounds and demonstrating consistent improvements in generalization performance, thereby validating both the theoretical analysis and practical efficacy.

Technology Category

• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We establish in-expectation and tail bounds on the generalization error of representation learning type algorithms. The bounds are in terms of the relative entropy between the distribution of the representations extracted from the training and"test'' datasets and a data-dependent symmetric prior, i.e., the Minimum Description Length (MDL) of the latent variables for the training and test datasets. Our bounds are shown to reflect the"structure"and"simplicity'' of the encoder and significantly improve upon the few existing ones for the studied model. We then use our in-expectation bound to devise a suitable data-dependent regularizer; and we investigate thoroughly the important question of the selection of the prior. We propose a systematic approach to simultaneously learning a data-dependent Gaussian mixture prior and using it as a regularizer. Interestingly, we show that a weighted attention mechanism emerges naturally in this procedure. Our experiments show that our approach outperforms the now popular Variational Information Bottleneck (VIB) method as well as the recent Category-Dependent VIB (CDVIB).

Problem

• Generalization error bounds for representation learning
• Data-dependent Gaussian mixture priors
• Improvement over Variational Information Bottleneck methods

Innovation

• Data-dependent Gaussian mixture priors
• Minimum Description Length regularization
• Weighted attention mechanism integration