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We address the problem of learning the dynamics of an unknown non-parametricsystem linking a target and a feature time series. The feature time series ismeasured on a sparse and irregular grid, while we have access to only a fewpoints of the target time series. Once learned, we can use these dynamics topredict values of the target from the previous values of the feature timeseries. We frame this task as learning the solution map of a controlleddifferential equation (CDE). By leveraging the rich theory of signatures, weare able to cast this non-linear problem as a high-dimensional linearregression. We provide an oracle bound on the prediction error which exhibitsexplicit dependencies on the individual-specific sampling schemes. Ourtheoretical results are illustrated by simulations which show that our methodoutperforms existing algorithms for recovering the full time series while beingcomputationally cheap. We conclude by demonstrating its potential on real-worldepidemiological data.

Learning the Dynamics of Sparsely Observed Interacting Systems