Volker Tresp, Thomas Briegel
We consider neural network models for stochastic nonlinear dynamical systems where measurements of the variable of interest are only avail(cid:173) able at irregular intervals i.e. most realizations are missing. Difficulties arise since the solutions for prediction and maximum likelihood learn(cid:173) ing with missing data lead to complex integrals, which even for simple cases cannot be solved analytically. In this paper we propose a spe(cid:173) cific 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 us(cid:173) ing 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.