# PAC Bayesian Performance Guarantees for Deep (Stochastic) Networks in Medical Imaging

arXiv: https://arxiv.org/abs/2104.05600 · HTML: https://mlsanity.com/paper/2104.05600/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 56 references that are in the map.
- First posted on arXiv 12 Apr 2021.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1902.03368/) (2019)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [Tighter risk certificates for neural networks](https://mlsanity.com/paper/2007.12911/) (2020)
- [Data-Dependent Stability of Stochastic Gradient Descent](https://mlsanity.com/paper/1703.01678/) (2017)
- [Generalization Bounds of SGLD for Non-convex Learning: Two Theoretical Viewpoints](https://mlsanity.com/paper/1707.05947/) (2017)
- [Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors](https://mlsanity.com/paper/1712.09376/) (2017)
- [In Search of Robust Measures of Generalization](https://mlsanity.com/paper/2010.11924/) (2020)
- [On the role of data in PAC-Bayes bounds](https://mlsanity.com/paper/2006.10929/) (2020)
- [Risk Bounds for the Majority Vote: From a PAC-Bayesian Analysis to a Learning Algorithm](https://mlsanity.com/paper/1503.08329/) (2015)
- [A PAC-Bayesian Tutorial with A Dropout Bound](https://mlsanity.com/paper/1307.2118/) (2013)
- [Unreasonable Effectiveness of Learning Neural Networks: From Accessible States and Robust Ensembles to Basic Algorithmic Schemes](https://mlsanity.com/paper/1605.06444/) (2016)
- [Subdominant Dense Clusters Allow for Simple Learning and High Computational Performance in Neural Networks with Discrete Synapses](https://mlsanity.com/paper/1509.05753/) (2015)
- [PAC-Bayes with Backprop](https://mlsanity.com/paper/1908.07380/) (2019)
- [Learning Gaussian Processes by Minimizing PAC-Bayesian Generalization Bounds](https://mlsanity.com/paper/1810.12263/) (2018)
- [PAC-Bayes bounds for stable algorithms with instance-dependent priors](https://mlsanity.com/paper/1806.06827/) (2018)

## Built on by (most cited first, 3 of 3)

- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)
- [FedHPL: Efficient Heterogeneous Federated Learning with Prompt Tuning and Logit Distillation](https://mlsanity.com/paper/2405.17267/) (2024)
- [Modeling Non-Cooperative Dialogue: Theoretical and Empirical Insights](https://mlsanity.com/paper/2207.07255/) (2022)

## Abstract (arXiv)

Application of deep neural networks to medical imaging tasks has in some sense become commonplace. Still, a "thorn in the side" of the deep learning movement is the argument that deep networks are prone to overfitting and are thus unable to generalize well when datasets are small (as is common in medical imaging tasks). One way to bolster confidence is to provide mathematical guarantees, or bounds, on network performance after training which explicitly quantify the possibility of overfitting. In this work, we explore recent advances using the PAC-Bayesian framework to provide bounds on generalization error for large (stochastic) networks. While previous efforts focus on classification in larger natural image datasets (e.g., MNIST and CIFAR-10), we apply these techniques to both classification and segmentation in a smaller medical imagining dataset: the ISIC 2018 challenge set. We observe the resultant bounds are competitive compared to a simpler baseline, while also being more explainable and alleviating the need for holdout sets.