Neural Controlled Differential Equations for Irregular Time Series
This addresses the limitation of neural ODEs in handling partially-observed, irregular time series for applications like healthcare or finance, representing a novel method rather than an incremental improvement.
The paper tackles the problem of modeling irregularly-sampled time series by introducing neural controlled differential equations, which adjust trajectories based on observations, achieving state-of-the-art performance in empirical studies.
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no mechanism for adjusting the trajectory based on subsequent observations. Here, we demonstrate how this may be resolved through the well-understood mathematics of \emph{controlled differential equations}. The resulting \emph{neural controlled differential equation} model is directly applicable to the general setting of partially-observed irregularly-sampled multivariate time series, and (unlike previous work on this problem) it may utilise memory-efficient adjoint-based backpropagation even across observations. We demonstrate that our model achieves state-of-the-art performance against similar (ODE or RNN based) models in empirical studies on a range of datasets. Finally we provide theoretical results demonstrating universal approximation, and that our model subsumes alternative ODE models.