Path Imputation Strategies for Signature Models

The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning. However real-world temporal data is typically discretised, and must first be transformed into a continuous path before signature techniques can be applied. We characterise this as an imputation problem, and empirically assess the impact of various imputation techniques when applying signatures to irregular time series data. In our experiments, we find that the choice of imputation drastically affects shallow signature models, whereas deeper architectures are more robust. We also observe that uncertainty-aware predictions are overall beneficial, even compared to the uncertainty-aware training of Gaussian process (GP) adapters. Hence, we propose an extension of GP adapters by integrating uncertainty to the prediction step. This leads to competitive performance in general, and improves robustness in signature models in particular.