Project summary

We consider longitudinal data from clinical cohorts with few individuals. For these, a latent representation is obtained via neural networks and modeled by differential equations. To enable individual dynamic models based on only a small number of observations, individuals similar to each other are determined according to the latent dynamics. Furthermore, also selection of necessary model components is performed locally. For better reflecting unobserved influences, we will consider stochastic differential equations. Development of the corresponding filtering theory will incorporate random and state-dependent observation time points. We will derive error bounds for the estimator of the latent state, which will also serve as a basis for locally performing model selection.

Our methods

• Combining knowledge- and data-driven modeling
• Differential equations
• Neural networks
• Local perspective