🤖 AI Summary
This work addresses uncertainty quantification in neural networks to enhance predictive reliability and calibration. We propose Monte Carlo Noise Injection (MCNI), a novel paradigm that injects stochastic noise into model weights during training and estimates uncertainty via multiple forward passes at inference time. Crucially, we provide the first theoretical proof that this noise-injection mechanism is strictly equivalent to Bayesian inference under a deep Gaussian process (DGP) prior—thereby establishing a rigorous Bayesian foundation for weight randomization methods. Compared to conventional approaches such as Dropout and ensemble methods, MCNI achieves significantly improved accuracy in uncertainty estimation and superior calibration of predictive confidence across both regression and classification tasks. The method combines theoretical soundness with practical efficiency, requiring no architectural modifications or substantial computational overhead beyond standard Monte Carlo sampling.
📝 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.