Probabilistic survival predictions from models trained with Maximum
Likelihood Estimation (MLE) can have high, and sometimes unacceptably high
variance. The field of meteorology, where the paradigm of maximizing sharpness
subject to calibration is popular, has addressed this problem by using scoring
rules beyond MLE, such as the Continuous Ranked Probability Score (CRPS). In
this paper we present the \emph{Survival-CRPS}, a generalization of the CRPS to
the survival prediction setting, with right-censored and interval-censored
variants. We evaluate our ideas on the mortality prediction task using two
different Electronic Health Record (EHR) data sets (STARR and MIMIC-III)
covering millions of patients, with suitable deep neural network architectures:
a Recurrent Neural Network (RNN) for STARR and a Fully Connected Network (FCN)
for MIMIC-III. We compare results between the two scoring rules while keeping
the network architecture and data fixed, and show that models trained with
Survival-CRPS result in sharper predictive distributions compared to those
trained by MLE, while still maintaining calibration.

本文提出了 Survival-CRPS，它是一种广义的连续秩概率得分，用于生存预测设置的正确或区间截断变体，并评估了两个电子健康记录数据集上的死亡率预测任务的效果，结果表明训练 CRPS 得分的模型相较于 MLE 训练的模型拥有更加尖锐的预测分布并保持校准。