# Uncertainty Estimation via Stochastic Batch Normalization

arXiv: https://arxiv.org/abs/1802.04893 · HTML: https://mlsanity.com/paper/1802.04893/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 11 of 11)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [SegmentMeIfYouCan: A Benchmark for Anomaly Segmentation](https://mlsanity.com/paper/2104.14812/) (2021)
- [Uncertainty-Aware Deep Co-training for Semi-supervised Medical Image Segmentation](https://mlsanity.com/paper/2111.11629/) (2021)
- [U-LanD: Uncertainty-Driven Video Landmark Detection](https://mlsanity.com/paper/2102.01586/) (2021)
- [Interactive Medical Image Segmentation with Self-Adaptive Confidence Calibration](https://mlsanity.com/paper/2111.07716/) (2021)
- [Detecting and Learning the Unknown in Semantic Segmentation](https://mlsanity.com/paper/2202.08700/) (2022)
- [Uncertainty-Aware Segmentation Quality Prediction via Deep Learning Bayesian Modeling: Comprehensive Evaluation and Interpretation on Skin Cancer and Liver Segmentation](https://mlsanity.com/paper/2508.01460/) (2025)
- [TransMorph: Transformer for unsupervised medical image registration](https://mlsanity.com/paper/2111.10480/) (2021)
- [Uncertainty Quantification for Image-based Traffic Prediction across Cities](https://mlsanity.com/paper/2308.06129/) (2023)
- [Monte Carlo Stochastic Depth for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/2604.12719/) (2026)
- [Controllable Diversity in Normalization-Based Implicit Ensembles via Softmax-Temperature Modulation](https://mlsanity.com/paper/2607.23860/) (2026)

## Abstract (arXiv)

In this work, we investigate Batch Normalization technique and propose its probabilistic interpretation. We propose a probabilistic model and show that Batch Normalization maximazes 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.