  We investigate regression for variable length sequential data containing
missing samples and introduce a novel tree architecture based on the Long
Short-Term Memory (LSTM) networks. In our architecture, we employ a variable
number of LSTM networks, which use only the existing inputs in the sequence, in
a tree-like architecture without any statistical assumptions or imputations on
the missing data, unlike all the previous approaches. In particular, we
incorporate the missingness information by selecting a subset of these LSTM
networks based on "presence-pattern" of a certain number of previous inputs.
From the mixture of experts perspective, we train different LSTM networks as
our experts for various missingness patterns and then combine their outputs to
generate the final prediction. We also provide the computational complexity
analysis of the proposed architecture, which is in the same order of the
complexity of the conventional LSTM architectures for the sequence length. Our
method can be readily extended to similar structures such as GRUs, RNNs as
remarked in the paper. In the experiments, we achieve significant performance
improvements with respect to the state-of-the-art methods for the well-known
financial and real life datasets.
