Neural network modelling with input uncertainty:theory and application


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.

Publication DOI:
Divisions: ?? 50811700Jl ??
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: The original publication is available at
Uncontrolled Keywords: Bayesian inference methods,neural networks,noise,errors in variable,Bayesian neural network framework,input noise,noise process exists,noiseless input,Markov chain Monte Carlo,satellite radar backscatter system,sea surface wind vectors,Information Systems,Signal Processing,Electrical and Electronic Engineering
Publication ISSN: 1573-109X
Last Modified: 27 Jun 2024 07:36
Date Deposited: 25 Nov 2010 13:14
Full Text Link:
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://www.spri ... 3127m600401485/ (Publisher URL)
PURE Output Type: Article
Published Date: 2000
Authors: Cornford, Dan (ORCID Profile 0000-0001-8787-6758)
Wright, W.A.
Ramage, Guillaume
Nabney, Ian T. (ORCID Profile 0000-0003-1513-993X)



Version: Accepted Version

Export / Share Citation


Additional statistics for this record