  We present ARU, an Adaptive Recurrent Unit for streaming adaptation of deep
globally trained time-series forecasting models. The ARU combines the
advantages of learning complex data transformations across multiple time series
from deep global models, with per-series localization offered by closed-form
linear models. Unlike existing methods of adaptation that are either
memory-intensive or non-responsive after training, ARUs require only fixed
sized state and adapt to streaming data via an easy RNN-like update operation.
The core principle driving ARU is simple --- maintain sufficient statistics of
conditional Gaussian distributions and use them to compute local parameters in
closed form. Our contribution is in embedding such local linear models in
globally trained deep models while allowing end-to-end training on the one
hand, and easy RNN-like updates on the other. Across several datasets we show
that ARU is more effective than recently proposed local adaptation methods that
tax the global network to compute local parameters.
