Spatio-temporal correlated noise in multi-output neural networks

In this paper, supposing a Gaussian noise model, we study the problem of multi-output nonlinear regression using multilayer perceptrons (MLP) when the noise in each output is a correlated autoregressive time series and there is a spatial correlation between different output noise sources. We show that using a maximum likelihood approach, the noise parameters can be determined simultaneously with the network weights and used to improve the network generalization performance. For two special cases of first and second order AR noise, the appropriate cost functions to minimize them are derived