Recursive input and state estimation: A general framework for learning from time series with missing data

Time series with missing data are signals encountered in important settings\nfor machine learning. Some of the most successful prior approaches for modeling\nsuch time series are based on recurrent neural networks that transform the\ninput and previous state to account for the missing observations, and then\ntreat the transformed signal in a standard manner.\n In this paper, we introduce a single unifying framework, Recursive Input and\nState Estimation (RISE), for this general approach and reformulate existing\nmodels as specific instances of this framework. We then explore additional\nnovel variations within the RISE framework to improve the performance of any\ninstance. We exploit representation learning techniques to learn latent\nrepresentations of the signals used by RISE instances. We discuss and develop\nvarious encoding techniques to learn latent signal representations. We\nbenchmark instances of the framework with various encoding functions on three\ndata imputation datasets, observing that RISE instances always benefit from\nencoders that learn representations for numerical values from the digits into\nwhich they can be decomposed.\n