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Abstract:
We consider neural network models for stochastic nonlinear
dynamical systems where measurements of the variable of interest
are only available at irregular intervals i.e. most realizations
are missing. Difficulties arise since the solutions for prediction
and maximum likelihood learning with missing data lead to complex
integrals, which even for simple cases cannot be solved
analytically. In this paper we propose a specific combination of a
nonlinear recurrent neural predictive model and a linear error
model which leads to tractable prediction and maximum likelihood
adaptation rules. In particular, the recurrent neural network can
be trained using the real-time recurrent learning rule and the
linear error model can be trained by an EM adaptation rule,
implemented using forward-backward Kalman filter equations. The
model is applied to predict the glucose/insulin metabolism of a
diabetic patient where blood glucose measurements are only
available a few times a day at irregular intervals. The new model
shows considerable improvement with respect to both recurrent
neural networks trained with teacher forcing or in a free running
mode and various linear models.
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