  Recurrent neural networks (RNNs) are instrumental in modelling sequential and
time-series data. Yet, when using RNNs to inform decision-making, predictions
by themselves are not sufficient; we also need estimates of predictive
uncertainty. Existing approaches for uncertainty quantification in RNNs are
based predominantly on Bayesian methods; these are computationally prohibitive,
and require major alterations to the RNN architecture and training.
Capitalizing on ideas from classical jackknife resampling, we develop a
frequentist alternative that: (a) does not interfere with model training or
compromise its accuracy, (b) applies to any RNN architecture, and (c) provides
theoretical coverage guarantees on the estimated uncertainty intervals. Our
method derives predictive uncertainty from the variability of the (jackknife)
sampling distribution of the RNN outputs, which is estimated by repeatedly
deleting blocks of (temporally-correlated) training data, and collecting the
predictions of the RNN re-trained on the remaining data. To avoid exhaustive
re-training, we utilize influence functions to estimate the effect of removing
training data blocks on the learned RNN parameters. Using data from a critical
care setting, we demonstrate the utility of uncertainty quantification in
sequential decision-making.
