# Uncertainty Quantification in CNN Through the Bootstrap of Convex Neural Networks

arXiv: https://arxiv.org/abs/2604.11833 · HTML: https://mlsanity.com/paper/2604.11833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 11 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Randomized Prior Functions for Deep Reinforcement Learning](https://mlsanity.com/paper/1806.03335/) (2018)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Learning Sparse Feature Representations using Probabilistic Quadtrees and Deep Belief Nets](https://mlsanity.com/paper/1509.03413/) (2015)
- [Convexified Convolutional Neural Networks](https://mlsanity.com/paper/1609.01000/) (2016)

## Abstract (arXiv)

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.