Uncertainty Quantification With Noise Injection in Neural Networks: A Bayesian Perspective

TL;DR

This paper links noise injection in neural networks to Bayesian uncertainty quantification, proposing a Monte Carlo Noise Injection method that improves prediction confidence estimation in regression and classification tasks.

Contribution

It establishes a theoretical connection between noise injection and Bayesian inference, introducing a novel MCNI method for uncertainty quantification in neural networks.

Findings

MCNI outperforms baseline models in experiments

Noise injection is equivalent to Bayesian inference on deep Gaussian processes

Method improves uncertainty estimation in neural network predictions

Abstract

Model uncertainty quantification involves measuring and evaluating the uncertainty linked to a model's predictions, helping assess their reliability and confidence. Noise injection is a technique used to enhance the robustness of neural networks by introducing randomness. In this paper, we establish a connection between noise injection and uncertainty quantification from a Bayesian standpoint. We theoretically demonstrate that injecting noise into the weights of a neural network is equivalent to Bayesian inference on a deep Gaussian process. Consequently, we introduce a Monte Carlo Noise Injection (MCNI) method, which involves injecting noise into the parameters during training and performing multiple forward propagations during inference to estimate the uncertainty of the prediction. Through simulation and experiments on regression and classification tasks, our method demonstrates superior performance compared to the baseline model.