  For recurrent neural networks trained on time series with target and
exogenous variables, in addition to accurate prediction, it is also desired to
provide interpretable insights into the data. In this paper, we explore the
structure of LSTM recurrent neural networks to learn variable-wise hidden
states, with the aim to capture different dynamics in multi-variable time
series and distinguish the contribution of variables to the prediction. With
these variable-wise hidden states, a mixture attention mechanism is proposed to
model the generative process of the target. Then we develop associated training
methods to jointly learn network parameters, variable and temporal importance
w.r.t the prediction of the target variable. Extensive experiments on real
datasets demonstrate enhanced prediction performance by capturing the dynamics
of different variables. Meanwhile, we evaluate the interpretation results both
qualitatively and quantitatively. It exhibits the prospect as an end-to-end
framework for both forecasting and knowledge extraction over multi-variable
data.
