Paper:
With a mortality rate of 5.4 million lives worldwide every year and a healthcare cost of more than 16 billion dollars in the USA alone, sepsis is one of the leading causes of hospital mortality and an increasing concern in the ageing western world. Recently, medical and technological advances have helped re-define the illness criteria of this disease, which is otherwise poorly understood by the medical society. Together with the rise of widely accessible Electronic Health Records, the advances in data mining and complex nonlinear algorithms are a promising avenue for the early detection of sepsis. This work contributes to the research effort in the field of automated sepsis detection with an open-access labelling of the medical MIMIC-III data set. Moreover, we propose MGP-AttTCN: a joint multitask Gaussian Process and attention-based deep learning model to early predict the occurrence of sepsis in an interpretable manner. We show that our model outperforms the current state-of-the-art and present evidence that different labelling heuristics lead to discrepancies in task difficulty.

Review:
The authors consider a combination of an Gaussian model and neural network learned together to be able to find specific Gaussian features that would predict sepsis in a more intuitive, interpretable way for a medical experts. Also, they have provided a new labelling for the MIMIC-III dataset, which is of great value.
Usually constraining the feature space reduces the accuracy, as one tends to miss important features. However, here, one is using a Gaussian model to generate a feature space that is easier to train with a neural network (by filling the sparse data by Gaussian process interpolation) but also augment the dataset.
The author report that his improves prediction. Unfortunately, I did not find tables of solutions where one could the actual impact. The authors should include a numerical table of their result comparison results.  Now there is only a narrative in section 5.3 and an image showing that at different covariance times, different feature groups starts to interpret the results. Obviously, a question arises if the model would perform even better with a combination of covariance times, or is there some covariance time range that is missing that would improve the result even more.
The Gaussian model creates smooth interpolation of data spaces and also forces the training to look at corresponding smoothened features - that are very good for human eyes. However, there are situations (like the detecting heart beat from a video from a head moving with a recoil from the blood rushing to the brain) in where the signal is too weak for human to see, but is definitely there for a computer.  I would state that this as interpretable,  as an explicitly visible signal would be. Even  shorter time constant signal might be valuable as well, but it would not be visible here...  It seems that in sepsis, it was a good idea, as it improves the result compared to the situation of not using the Gaussian model. 
One has to be careful to state that this would address the interpretability of the results. Gaussian process by itself is not giving understanding nor interpretability as it is too general. But it can make the provided solution "teachable" to a human expert by showing what visible features one can track.
Compare this to a situation where one is using physical model to regularize detection. It has the analogous two model structure like the one in the manuscript. In https://xbpeng.github.io/projects/SFV/index.html the authors of the paper report that that one can achieve a better pose estimation by constraining the pose to only those that are achievable by a physical model based policy trained by reinforcement learning. This one is able to "interpret" the pose.
As a summary, the authors have done solid and valuable work in improving the accuracy detection. They should have a more formal way to present the results and baseline comparisions as tables. On the explainability and interpretability, there remains a lot of interpretations and one has lots of explaining to do, even after this manuscript.