  In many forecasting applications, it is valuable to predict not only the
value of a signal at a certain time point in the future, but also the values
leading up to that point. This is especially true in clinical applications,
where the future state of the patient can be less important than the patient's
overall trajectory. This requires multi-step forecasting, a forecasting variant
where one aims to predict multiple values in the future simultaneously.
Standard methods to accomplish this can propagate error from prediction to
prediction, reducing quality over the long term. In light of these challenges,
we propose multi-output deep architectures for multi-step forecasting in which
we explicitly model the distribution of future values of the signal over a
prediction horizon. We apply these techniques to the challenging and clinically
relevant task of blood glucose forecasting. Through a series of experiments on
a real-world dataset consisting of 550K blood glucose measurements, we
demonstrate the effectiveness of our proposed approaches in capturing the
underlying signal dynamics. Compared to existing shallow and deep methods, we
find that our proposed approaches improve performance individually and capture
complementary information, leading to a large improvement over the baseline
when combined (4.87 vs. 5.31 absolute percentage error (APE)). Overall, the
results suggest the efficacy of our proposed approach in predicting blood
glucose level and multi-step forecasting more generally.
