Theoretical Analysis of Measure Consistency Regularization for Partially Observed Data

2026-02-01

AI Summary

This work addresses the degradation of model generalization caused by partially observed data, such as missing features or modalities. From the perspective of neural network distance, it provides a theoretical analysis of Measure Consistency Regularization (MCR), for the first time revealing the mechanism by which MCR enhances both data imputation quality and generalization performance. The study rigorously establishes the conditions under which MCR’s generalization advantage holds. Building on these insights, the authors propose a duality-gap-based early stopping strategy that preserves MCR’s benefits while mitigating overfitting. Extensive experiments across diverse real-world multimodal datasets and network architectures demonstrate the effectiveness and broad applicability of the proposed approach.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Multi-modal Vision
• Natural Language Processing: Language Grounding & Multi-modal NLP

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

The problem of corrupted data, missing features, or missing modalities continues to plague the modern machine learning landscape. To address this issue, a class of regularization methods that enforce consistency between imputed and fully observed data has emerged as a promising approach for improving model generalization, particularly in partially observed settings. We refer to this class of methods as Measure Consistency Regularization (MCR). Despite its empirical success in various applications, such as image inpainting, data imputation and semi-supervised learning, a fundamental understanding of the theoretical underpinnings of MCR remains limited. This paper bridges this gap by offering theoretical insights into why, when, and how MCR enhances imputation quality under partial observability, viewed through the lens of neural network distance. Our theoretical analysis identifies the term responsible for MCR's generalization advantage and extends to the imperfect training regime, demonstrating that this advantage is not always guaranteed. Guided by these insights, we propose a novel training protocol that monitors the duality gap to determine an early stopping point that preserves the generalization benefit. We then provide detailed empirical evidence to support our theoretical claims and to show the effectiveness and accuracy of our proposed stopping condition. We further provide a set of real-world data simulations to show the versatility of MCR under different model architectures designed for different data sources.

Problem

• partially observed data
• measure consistency regularization
• missing features
• corrupted data
• generalization

Innovation

• Measure Consistency Regularization
• partial observability
• theoretical analysis
• duality gap
• early stopping