  Missing data is a ubiquitous problem. It is especially challenging in medical
settings because many streams of measurements are collected at different - and
often irregular - times. Accurate estimation of those missing measurements is
critical for many reasons, including diagnosis, prognosis and treatment.
Existing methods address this estimation problem by interpolating within data
streams or imputing across data streams (both of which ignore important
information) or ignoring the temporal aspect of the data and imposing strong
assumptions about the nature of the data-generating process and/or the pattern
of missing data (both of which are especially problematic for medical data). We
propose a new approach, based on a novel deep learning architecture that we
call a Multi-directional Recurrent Neural Network (M-RNN) that interpolates
within data streams and imputes across data streams. We demonstrate the power
of our approach by applying it to five real-world medical datasets. We show
that it provides dramatically improved estimation of missing measurements in
comparison to 11 state-of-the-art benchmarks (including Spline and Cubic
Interpolations, MICE, MissForest, matrix completion and several RNN methods);
typical improvements in Root Mean Square Error are between 35% - 50%.
Additional experiments based on the same five datasets demonstrate that the
improvements provided by our method are extremely robust.
