Set Functions for Time Series

Nevertheless, in many application domains, in particular healthcare (Y adav et al., 2018), measurements might not necessarily be observed at a regular rate or could be misaligned. Moreover, the presence or absence of a measurement and its observation frequency may carry information of its own (Little & Rubin, 2014), such that imputing the missing values is not always desired. While some algorithms can be readily applied to datasets with varying length, these methods usually assume regular sampling of the data and/or require the measurements across modalities to be aligned/synchronized, preventing their application to the aforementioned settings. Existing approaches for unaligned measurements, by contrast, typically rely on imputation to obtain a regularly-sampled version of a data set for classification. Learning a suitable imputation scheme, however, requires understanding the underlying dynamics of a system; this task is significantly more complicated and not necessarily required when classification is the main goal. Furthermore, even though a decoupled imputation scheme followed by classification is generally more scalable, it may lose information that is relevant for prediction tasks. Approaches that jointly optimize both tasks add a large computational overhead, thus suffering from poor scalability or high memory requirements. Our method is motivated by the understanding that, while RNNs and similar architectures are well suited for capturing and modelling the dynamics of a time series and thus excel at tasks such as forecasting, retaining the order of an input sequence can even be a disadvantage in classification scen-1 arXiv:1909.12064v1