  Time series with missing data are signals encountered in important settings
for machine learning. Some of the most successful prior approaches for modeling
such time series are based on recurrent neural networks that transform the
input and previous state to account for the missing observations, and then
treat the transformed signal in a standard manner.
  In this paper, we introduce a single unifying framework, Recursive Input and
State Estimation (RISE), for this general approach and reformulate existing
models as specific instances of this framework. We then explore additional
novel variations within the RISE framework to improve the performance of any
instance. We exploit representation learning techniques to learn latent
representations of the signals used by RISE instances. We discuss and develop
various encoding techniques to learn latent signal representations. We
benchmark instances of the framework with various encoding functions on three
data imputation datasets, observing that RISE instances always benefit from
encoders that learn representations for numerical values from the digits into
which they can be decomposed.
