It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise or corruption. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which allows for input noise given that some model of the noise process exists. In the limit where this noise process is small and symmetric it is shown, using the Laplace approximation, that there is an additional 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 Markov Chain Monte Carlo methods, it is demonstrated that it is possible to infer the unbiassed regression over the noiseless input.
|Title of host publication||Proceedings of the 1998 IEEE Signal Processing Society Workshop, Neural Networks for Signal Processing VIII, 1998|
|Place of Publication||Cambridge, UK|
|Number of pages||10|
|Publication status||Published - 2 Sep 1998|
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- Bayesian inference methods
- neural networks
- Bayesian neural network
- Laplace approximation
- Bayesian error
- Markov Chain Monte Carlo method
- unbiassed regression
- noiseless input