  Bidirectional recurrent neural networks (RNN) are trained to predict both in
the positive and negative time directions simultaneously. They have not been
used commonly in unsupervised tasks, because a probabilistic interpretation of
the model has been difficult. Recently, two different frameworks, GSN and NADE,
provide a connection between reconstruction and probabilistic modeling, which
makes the interpretation possible. As far as we know, neither GSN or NADE have
been studied in the context of time series before. As an example of an
unsupervised task, we study the problem of filling in gaps in high-dimensional
time series with complex dynamics. Although unidirectional RNNs have recently
been trained successfully to model such time series, inference in the negative
time direction is non-trivial. We propose two probabilistic interpretations of
bidirectional RNNs that can be used to reconstruct missing gaps efficiently.
Our experiments on text data show that both proposed methods are much more
accurate than unidirectional reconstructions, although a bit less accurate than
a computationally complex bidirectional Bayesian inference on the
unidirectional RNN. We also provide results on music data for which the
Bayesian inference is computationally infeasible, demonstrating the scalability
of the proposed methods.
