  In time-series forecasting, future target values may be affected by both
intrinsic and extrinsic effects. When forecasting blood glucose, for example,
intrinsic effects can be inferred from the history of the target signal alone
(\textit{i.e.} blood glucose), but accurately modeling the impact of extrinsic
effects requires auxiliary signals, like the amount of carbohydrates ingested.
Standard forecasting techniques often assume that extrinsic and intrinsic
effects vary at similar rates. However, when auxiliary signals are generated at
a much lower frequency than the target variable (e.g., blood glucose
measurements are made every 5 minutes, while meals occur once every few hours),
even well-known extrinsic effects (e.g., carbohydrates increase blood glucose)
may prove difficult to learn. To better utilize these \textit{sparse but
informative variables} (SIVs), we introduce a novel encoder/decoder forecasting
approach that accurately learns the per-timepoint effect of the SIV, by (i)
isolating it from intrinsic effects and (ii) restricting its learned effect
based on domain knowledge. On a simulated dataset pertaining to the task of
blood glucose forecasting, when the SIV is accurately recorded our approach
outperforms baseline approaches in terms of rMSE (13.07 [95% CI: 11.77,14.16]
vs. 14.14 [12.69,15.27]). In the presence of a corrupted SIV, the proposed
approach can still result in lower error compared to the baseline but the
advantage is reduced as noise increases. By isolating their effects and
incorporating domain knowledge, our approach makes it possible to better
utilize SIVs in forecasting.
