Reconstructing common latent input from time series with the mapper-coach network and error backpropagation
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A two-module, feedforward neural network architecture called mapper-coach network has been introduced to reconstruct an unobserved, continuous latent variable input, driving two observed dynamical systems. The method has been demonstrated on time series generated by two chaotic logistic maps driven by a hidden third one. The network has been trained to predict one of the observed time series based on its own past and on the other observed time series by error-back propagation. It was shown, that after this prediction have been learned successfully, the activity of the bottleneck neuron, connecting the mapper and the coach module, correlates strongly with the latent common input variable. The method has the potential to reveal hidden components of dynamical systems, where experimental intervention is not possible.
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