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We present Monte-Carlo generalized EM equations for learning in non-linear state space models. The difficulties lie in the Monte-Carlo E-step which consists of sampling from the posterior distribution of the hidden variables given the observations. The new idea presented in this paper is to generate samples from a Gaussian approximation to the true… (More)

We study the application of neural networks to modeling the blood glucose metabolism of a diabetic. In particular we consider recurrent neural networks and time series convolution neural networks which we compare to linear models and to nonlinear compartment models. We include a linear error model to take into account the uncertainty in the system and for… (More)

We replace the commonly used Gaussian noise model in nonlinear regression by a more flexible noise model based on the Student-t-distribution. The degrees of freedom of the t-distribution can be chosen such that as special cases either the Gaussian distribution or the Cauchy distribution are realized. The latter is commonly used in robust regression. Since… (More)

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. Dif£culties arise since the solutions for prediction and maximum likelihood learning with missing data lead to complex integrals, which even for simple cases… (More)

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