  The problem of real time prediction of blood glucose (BG) levels based on the
readings from a continuous glucose monitoring (CGM) device is a problem of
great importance in diabetes care, and therefore, has attracted a lot of
research in recent years, especially based on machine learning. An accurate
prediction with a 30, 60, or 90 minute prediction horizon has the potential of
saving millions of dollars in emergency care costs. In this paper, we treat the
problem as one of function approximation, where the value of the BG level at
time $t+h$ (where $h$ the prediction horizon) is considered to be an unknown
function of $d$ readings prior to the time $t$. This unknown function may be
supported in particular on some unknown submanifold of the $d$-dimensional
Euclidean space. While manifold learning is classically done in a
semi-supervised setting, where the entire data has to be known in advance, we
use recent ideas to achieve an accurate function approximation in a supervised
setting; i.e., construct a model for the target function. We use the
state-of-the-art clinically relevant PRED-EGA grid to evaluate our results, and
demonstrate that for a real life dataset, our method performs better than a
standard deep network, especially in hypoglycemic and hyperglycemic regimes.
One noteworthy aspect of this work is that the training data and test data may
come from different distributions.
