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.
(supervised by PI Binder)
Approaches for combining neural networks with differential equations (ODEs as well as SDEs). This will include approaches for model selection, to obtain patient-specific models.
(supervised by PI Schmidt)
Mathematical theory for guiding methods development, in a filtering framework, which will, e.g., provide error bounds and goodness-of-fit approaches for model selection.
Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center –
University of Freiburg