  The signature transform is a 'universal nonlinearity' on the space of
continuous vector-valued paths, and has received attention for use in machine
learning on time series. However, real-world temporal data is typically
observed at discrete points in time, and must first be transformed into a
continuous path before signature techniques can be applied. We make this step
explicit by characterising it as an imputation problem, and empirically assess
the impact of various imputation strategies when applying signature-based
neural nets to irregular time series data. For one of these strategies,
Gaussian process (GP) adapters, we propose an extension~(GP-PoM) that makes
uncertainty information directly available to the subsequent classifier while
at the same time preventing costly Monte-Carlo (MC) sampling. In our
experiments, we find that the choice of imputation drastically affects shallow
signature models, whereas deeper architectures are more robust. Next, we
observe that uncertainty-aware predictions (based on GP-PoM or indicator
imputations) are beneficial for predictive performance, even compared to the
uncertainty-aware training of conventional GP adapters. In conclusion, we have
demonstrated that the path construction is indeed crucial for signature models
and that our proposed strategy leads to competitive performance in general,
while improving robustness of signature models in particular.
