Uncertainty Estimation via Stochastic Batch Normalization

This repo contains code for our paper Uncertainty Estimation via Stochastic Batch Normalization.

Abstract

In this work, we investigate Batch Normalization technique and propose its probabilistic interpretation. We propose a probabilistic model and show that Batch Normalization maximizes the lower bound of its marginalized log-likelihood. Then, according to the new probabilistic model, we design an algorithm which acts consistently during train and test. However, inference becomes computationally inefficient. To reduce memory and computational cost, we propose Stochastic Batch Normalization -- an efficient approximation of proper inference procedure. This method provides us with a scalable uncertainty estimation technique. We demonstrate the performance of Stochastic Batch Normalization on popular architectures (including deep convolutional architectures: VGG-like and ResNets) for MNIST and CIFAR-10 datasets.

Launch experiments

To reproduce the results follow the results.ipynb.

Accuracy and NLL results

Network	Method	Error%		NLL
		No SBN	SBN	No SBN	SBN
LeNet-5	SBN	---	0.53	---	0.025
	Deep Ensembles	0.40	0.40	0.016	0.015
	Dropout	0.42	0.42	0.014	0.014
VGG-11	SBN	---	5.76	---	0.302
	Deep Ensembles	4.81	4.81	0.191	0.162
	Dropout	5.32	5.38	0.155	0.149
ResNet-18	SBN	---	4.35	---	0.255
	Deep Ensembles	3.37	3.34	0.138	0.110

Uncertainty estimation

To estimate uncertainty we calculate entropy of predictive distribution on out-of-domain data.

LeNet-5 on notMNIST	ResNet-18 on CIFAR5	VGG-11 on CIFAR5

Citation

If you found this code useful please cite our paper

@article{stochbn2018,
  title={Uncertainty Estimation via Stochastic Batch Normalization},
  author={Atanov, Andrei and Ashukha, Arsenii and Molchanov, Dmitry and Neklyudov, Kirill and Vetrov, Dmitry},
  journal={arXiv preprint arXiv:1802.04893},
  year={2018}
}