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The signature transform is a 'universal nonlinearity' on the space ofcontinuous vector-valued paths, and has received attention for use in machinelearning on time series. However, real-world temporal data is typicallyobserved at discrete points in time, and must first be transformed into acontinuous path before signature techniques can be applied. We make this stepexplicit by characterising it as an imputation problem, and empirically assessthe impact of various imputation strategies when applying signature-basedneural nets to irregular time series data. For one of these strategies,Gaussian process (GP) adapters, we propose an extension~(GP-PoM) that makesuncertainty information directly available to the subsequent classifier whileat the same time preventing costly Monte-Carlo (MC) sampling. In ourexperiments, we find that the choice of imputation drastically affects shallowsignature models, whereas deeper architectures are more robust. Next, weobserve that uncertainty-aware predictions (based on GP-PoM or indicatorimputations) are beneficial for predictive performance, even compared to theuncertainty-aware training of conventional GP adapters. In conclusion, we havedemonstrated that the path construction is indeed crucial for signature modelsand that our proposed strategy leads to competitive performance in general,while improving robustness of signature models in particular.

Path Imputation Strategies for Signature Models of Irregular Time Series