This paper considers doing quantile regression on censored data using neural networks (NNs). This adds to the survival analysis toolkit by allowing direct prediction of the target variable, along with a distribution-free characterisation of uncertainty, using a flexible function approximator. We begin by showing how an algorithm popular in linear models can be applied to NNs. However, the resulting procedure is inefficient, requiring sequential optimisation of an individual NN at each desired quantile. Our major contribution is a novel algorithm that simultaneously optimises a grid of quantiles output by a single NN. To offer theoretical insight into our algorithm, we show firstly that it can be interpreted as a form of expectation-maximisation, and secondly that it exhibits a desirable `self-correcting' property. Experimentally, the algorithm produces quantiles that are better calibrated than existing methods on 10 out of 12 real datasets.

翻译：本文研究利用神经网络对删失数据进行分位数回归。该方法通过灵活的近似函数直接预测目标变量，并实现不确定性的无分布特征描述，从而拓展了生存分析工具集。我们首先展示了如何将线性模型中流行的算法应用于神经网络，但该过程效率低下，需要在每个目标分位数处对单个神经网络进行序列优化。我们的主要贡献在于提出一种新型算法，能够同步优化单个神经网络输出的分位数网格。为提供理论洞见，我们证明了该算法可被解释为一种期望最大化算法，并具有理想的"自校正"性质。实验结果表明，在12个真实数据集中，该算法生成的10个数据集的分位数校准度优于现有方法。