Uncertainty Estimation via Stochastic Batch Normalization

TL;DR

This paper introduces Stochastic Batch Normalization, a scalable method for uncertainty estimation in deep neural networks, based on a probabilistic interpretation of Batch Normalization, with demonstrated effectiveness on standard datasets.

Contribution

It provides a probabilistic interpretation of Batch Normalization and proposes Stochastic Batch Normalization as an efficient approximation for uncertainty estimation.

Findings

Effective uncertainty estimation on MNIST and CIFAR-10

Compatible with popular architectures like VGG and ResNets

Reduces computational cost compared to exact inference

Abstract

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.