Uncertainty Quantification in CNN Through the Bootstrap of Convex Neural Networks

2026-04-11

AI Summary

Convolutional neural networks (CNNs) face limited applicability in high-stakes scenarios due to the absence of efficient and theoretically grounded uncertainty quantification methods. This work proposes a novel framework that integrates convex neural networks with the bootstrap technique to deliver theoretically consistent uncertainty estimates. By enforcing structural convexity and incorporating a warm-start mechanism, the approach achieves significant computational savings while maintaining rigorous theoretical guarantees. The method is readily adaptable to arbitrary CNN architectures via transfer learning, offering—for the first time—theoretical consistency for CNN-based uncertainty quantification. Empirical evaluations across multiple image datasets demonstrate that the proposed approach substantially outperforms existing baselines and state-of-the-art methods, achieving both high predictive accuracy and computational efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Adversarial Attacks & Robustness
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Despite the popularity of Convolutional Neural Networks (CNN), the problem of uncertainty quantification (UQ) of CNN has been largely overlooked. Lack of efficient UQ tools severely limits the application of CNN in certain areas, such as medicine, where prediction uncertainty is critically important. Among the few existing UQ approaches that have been proposed for deep learning, none of them has theoretical consistency that can guarantee the uncertainty quality. To address this issue, we propose a novel bootstrap based framework for the estimation of prediction uncertainty. The inference procedure we use relies on convexified neural networks to establish the theoretical consistency of bootstrap. Our approach has a significantly less computational load than its competitors, as it relies on warm-starts at each bootstrap that avoids refitting the model from scratch. We further explore a novel transfer learning method so our framework can work on arbitrary neural networks. We experimentally demonstrate our approach has a much better performance compared to other baseline CNNs and state-of-the-art methods on various image datasets.

Problem

• Uncertainty Quantification
• Convolutional Neural Networks
• Theoretical Consistency
• Bootstrap
• Deep Learning

Innovation

• Uncertainty Quantification
• Bootstrap
• Convex Neural Networks
• Warm-start Optimization
• Transfer Learning