Creating artificial neural networks that generalize
Neural Networks
Bayesian methods for adaptive models
Bayesian methods for adaptive models
Neural Computation
Training with noise is equivalent to Tikhonov regularization
Neural Computation
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Outlier detection in scatterometer data: neural network approaches
Neural Networks - 2003 Special issue: Neural network analysis of complex scientific data: Astronomy and geosciences
A study of the effect of noise injection on the training of artificial neural networks
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
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It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which accounts for input noise provided that a model of the noise process exists. In the limit where the noise process is small and symmetric it is shown, using the Laplace approximation, that this method adds an extra term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable, and sampling this jointly with the network's weights, using a Markov chain Monte Carlo method, it is demonstrated that it is possible to infer the regression over the noiseless input. This leads to the possibility of training an accurate model of a system using less accurate, or more uncertain, data. This is demonstrated on both the, synthetic, noisy sine wave problem and a real problem of inferring the forward model for a satellite radar backscatter system used to predict sea surface wind vectors.