Paper:
In medicine, both ethical and monetary costs of incorrect predictions can be significant, and the complexity of the problems often necessitates increasingly complex models. Recent work has shown that changing just the random seed is enough for otherwise well-tuned deep neural networks to vary in their individual predicted probabilities. In light of this, we investigate the role of model uncertainty methods in the medical domain. Using recurrent neural network (RNN) ensembles and various Bayesian RNNs, we show that population-level metrics, such as AUC-PR, AUC-ROC, log-likelihood, and calibration error, do not capture model uncertainty. Meanwhile, the presence of significant variability in patient-specific predictions and optimal decisions motivates the need for capturing model uncertainty. Understanding the uncertainty for individual patients is an area with clear clinical impact, such as determining when a model decision is likely to be brittle. We further show that RNNs with only Bayesian embeddings can be a more efficient way to capture model uncertainty compared to ensembles, and we analyze how model uncertainty is impacted across individual input features and patient subgroups.

Review:
Thank you for an interesting read.
This paper is an experimental paper which argues the importance of epistemic/model uncertainty in applications for electronic health records (EHR). The main arguments are the following:
1. current metrics on dataset level cannot reveal uncertainty in prediction on personal level;
2. when evaluated on personal level, deterministic NNs with different random initialisations can produce very different predictions (thus require consideration of model uncertainty)
I am not exactly sure if ICLR is the best venue for this submission, as there is quite little innovation in modelling methodology, and the empirical analysis is domain specific. I feel this paper is more suitable to e.g. MLHC or MICCAI which focus on data analysis/machine learning methods applied to healthcare science.
Still I think the set of experiments in the paper is overall supportive to the main argument that the authors is trying to make. Possible improvements:
1. The histograms in Figure 3 & 4 clearly show that, deterministic NNs trained with different initialisations produces diverse predictions on individual patients. I commend the authors for presenting these visualisations, and I think it would be more useful to quantify this phenomenon on dataset level, e.g. compute the mean and variance of this variation of individual predictions.
2. I would expect to see an improvement of ECE for the Bayesian/deep ensemble models. The Table A.3 so marginal improvements, and I wonder how would this result support the author's claim? Also how do the ECE/ACE metrics look like when computed on sub-groups?
Apart from section 3.3, in general I think the paper writing is clear to me. The loss sensitive optimal decision method is interesting, but a lot of details are missing:
1. The presentation in section 3.3 is unclear, e.g. minimising eq. (4) w.r.t. what? What's the definition of decision region? Also what exactly is the mathematical form of the associated cost used in the experiments?
2. If I understand it correctly, in experiments the optimal thresholding method has only been applied to individual networks in the ensemble. If so what is the intention of discussing eq. (5) in the first place? Also it is unclear to me how this method performs in the deep ensemble/Bayesian RNN case. See e.g. https://arxiv.org/pdf/1805.03901.pdf for a relevant approach.