Modelling longitudinal data is both essential and inherently challenging. These datasets often exhibit complex, non-linear dynamics, feature time-varying covariates, and, in recent years, have become increasingly high-dimensional. Latent Neural Ordinary Differential Equations (ODEs) have gained recognition for their continuous-time formulation, making them a compelling choice for modelling such data. However, existing methods have notable limitations: they often overlook auxiliary covariates and control variables, key characteristics of longitudinal datasets, and are not equipped to handle missingness, a pervasive issue in real-world scenarios.
In this work, we introduce latent Neural cODE, a novel framework leveraging Neural Controlled ODEs to model the latent space of high-dimensional longitudinal data. Our approach incorporates auxiliary covariates seamlessly and explicitly addresses missingness mechanisms. Through various experiments, we demonstrate that latent Neural cODE achieves competitive performance across a range of scenarios. These advancements highlight latent Neural cODE's potential as a powerful and versatile framework for longitudinal data modelling.
