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Neural controlled differential equations (Neural CDEs) are a continuous-timeextension of recurrent neural networks (RNNs), achieving state-of-the-art(SOTA) performance at modelling functions of irregular time series. In order tointerpret discrete data in continuous time, current implementations rely onnon-causal interpolations of the data. This is fine when the whole time seriesis observed in advance, but means that Neural CDEs are not suitable for use in\textit{online prediction tasks}, where predictions need to be made inreal-time: a major use case for recurrent networks. Here, we show how thislimitation may be rectified. First, we identify several theoretical conditionsthat interpolation schemes for Neural CDEs should satisfy, such as boundednessand uniqueness. Second, we use these to motivate the introduction of newschemes that address these conditions, offering in particular measurability(for online prediction), and smoothness (for speed). Third, we empiricallybenchmark our online Neural CDE model on three continuous monitoring tasks fromthe MIMIC-IV medical database: we demonstrate improved performance on all tasksagainst ODE benchmarks, and on two of the three tasks against SOTA non-ODEbenchmarks.

Neural Controlled Differential Equations for Online Prediction Tasks